The following is imported from a now effectively defunct weblog of mine called ITLOG, and was a featured "Soapbox" item at TechRepublic. It is reproduced here with some modifications.
elegant (adj.): characterized by a lack of the gratuitous
C.A.R. Hoare: "There are two ways of constructing a software design. One way is to make it so simple that there are obviously no deficiencies. And the other way is to make it so complicated that there are no obvious deficiencies."
There's a long tradition of referring to the elegance of a system. In the IT industry, this tends most commonly to be applied to source code, and it is generally accepted that the more elegant it is, the better. Elegance is differentiated from other superficially good things in a number of ways, including the common assumption that elegance goes deeper, and applies more universally, while these other "good" things are only good within certain constraints.
For instance, "clever" source code is good for its cleverness, but can be bad for maintainability — mostly because clever code is often difficult to understand. Cleverness also falls short because of a simple principle famously articulated in an email signature of Brian Kernighan's: "Debugging is twice as hard as writing the code in the first place. Therefore, if you write the code as cleverly as possible, you are, by definition, not smart enough to debug it."
Another example is object oriented programming. Probably ninety-some percent of the competent programmers out there are thoroughly sold on the concept that OOP is the holy grail of programming techniques, and any further advances in programming techniques are just fine-tuning OOP techniques. I think this common perception is an outgrowth of twenty years of corporate influence on the evolution of programming, where large numbers of mediocre programmers end up handling the same codebase over the course of its lifespan. Two orthogonal systems of minimizing the damage a mediocre programmer can do to a project have been introduced to programming practice with a great deal of success: version control and object oriented programming.
Object oriented programming isn't the holy grail, though. It doesn't in any way aid with the creation of truly excellent code, in and of itself. It simply aids in the avoidance of truly atrocious code, and even then only in an aggregate view of a complex project. When you start drilling down to the individual bits and pieces of a complex software project that has passed through the hands of a great many mediocre programmers, you'll start seeing atrocious bits of code that limp along just well enough to keep working, as long as they're strictly encapsulated and separated from the rest of the codebase (except for its API, of course). Encapsulation and modularity are good things in general, but they aren't immutable axioms of goodness.
One of the trade-offs with object oriented programming is that it encourages repetitive action and tedious effort in writing code. Have a look at some "enterprise" class Java source code some time and start paying attention to how much of it is actual program logic, as contrasted with how much of it is scaffolding imposed on the source by Java's object-orientedness. In fact, if you really want to understand what's going on with object oriented programming and other superficially "good" things in programming, I recommend you start comparing how easily one can produce short, elegant code in various languages, and pay attention to why one language produces a shorter, more elegant solution than another. I think you'll find some surprising facts come to light.
Of course, it's true that brevity is not strictly synonymous with elegance. In fact, Perl golf — the practice of passing code around between programmers to see how short a given algorithm can be made — is a thoroughly gratuitous sport, concerned little, if at all, with elegance. In pursuing elegance, it is more important to be concise than merely brief. In a general sense, however, brevity of code does account for a decent quick and dirty measure of the potential elegance that can be eked out of a programming language, with length measured in number of distinct syntactic elements rather than the number of bytes of code: don't confuse the number of keystrokes in a variable assignment with the syntactic elements required to accomplish a variable assignment. Armed with that definition of the term "shorter", you should be able to make some meaningful comparisons of the elegance possible when working with various programming languages.
In particular, you might notice that without using any object oriented techniques, Common Lisp and Perl produce much shorter examples of certain algorithms than Java and C++. Even if you cut out all the object oriented scaffolding in the Java and C++ examples, you still typically end up with a lot more code, as measured in discrete syntactic elements. Things like lexical variables and anonymous blocks (or, roughly equivalently, lambdas) tend to make for much simpler, more elegant solutions than imposing rigorous OOP structure. In fact, the more you examine the matter and make such comparisons, the more I suspect you'll come to realize that OOP itself has nothing to do with producing elegance, and everything to do with limiting opportunity for mediocre programmers to produce cruft and introduce bugs.
Elegance is about the gratuitous — or, rather, avoiding the gratuitous. It's true that sometimes people disagree about which of two or more things is the "most elegant", but this arises from underlying assumptions rather than any true subjectivity of the principle. Each of us has a set of operating assumptions, some greater (meaning: bloated and cumbersome) than others. Where something conforms to one's expectations and assumptions, it is seen to not lack in elegance in that manner. Someone that does not have the same underlying assumptions might see the same thing as atrociously inelegant, but having a different set of assumptions would overlook similarly subjective quirks in another example that are, to the first person, inelegant.
Specifically, someone with assumptions derived from long indoctrination by the OOP crowd might overlook all the scaffolding imposed by a language like Java for using OOP techniques, and see something that takes up 50 lines of program logic and 150 lines of OOP scaffolding as elegant. Meanwhile, a long-time Perl hacker might take one look at that and see it as the inelegant monstrosity it is. This Perl hacker, on the other hand, might write 30 lines of procedural code to perform the same task, and the Java programmer might look at it and wonder why it isn't more modular, simplifying the program logic itself and making the whole thing more scalable for future code maintenance, thus rightly seeing the inelegance of the procedural hack the Perl programmer threw together.
This doesn't make elegance subjective: it only makes our individual perspectives on it subjective. If we can discard the assumptions of both the Java developer and the Perl hacker, and recognize the underlying principles of source code design that contributed elegance to each solution, we could probably turn the same set of solutions into something much, much simpler and more elegant, in terms of its program logic and cruft-weight. Unfortunately, languages like Java are not really suited to that sort of optimization for elegance: you really need a language more dynamic than that, such as Perl, Python, Ruby, or basically any Lisp. The more a language lets you define the language you're using on the fly, the more likely it is to allow an excellent programmer to produce elegance, which should really be the end goal of writing code, generally speaking: elegant solutions.
All really useful principles of programming, or systems design in general, seem to be practical, case-specific extrapolations from my fundamental definition of elegance. In short, they all seem to boil down to this one instruction: If it's gratuitous, find a way to get rid of it. For example, consider the Pragmatic Programmers' DRY principle — Don't Repeat Yourself. In short, it is a Good Thing to avoid repetitions of data and program logic in your code. Any time you find yourself having to repeat or rephrase something in your code, reinject data into your data model from wherever you have it stored, and so on, you're screwing up. Ask yourself whether DRY is really useful by reducing repetition in and of itself, or by reducing gratuitous repetition. After all, recursion and looping behavior might also fall within the definition of "repeat yourself", but I don't think anyone (sane) would ever recommend eliminating all loops and recursion from all programs. Sometimes, you just need your program to perform a given set of instructions on a long list of slightly different items. Often, loops and recursion make source code more elegant.
This ties in very nicely with the more general, more philosophical concept of aesthetics, and that provides some understanding of why it is possible to look at source code and, without yet consciously knowing what's wrong with it, have an immediate intuitive reaction to its inelegance. That's not to say that something can't be aesthetically pleasing without being perfect in its elegance, of course. Instead, the ability to recognize some characteristics of elegance is what leads to an aesthetically pleasing perception of the subject.
Elegance is not about aesthetics. Rather, aesthetics is about elegance. Ostentation lacks aesthetic appeal, and is inelegant (read: "tacky"), because it's gratuitous. Simplicity is often not elegant either: if something is too simple, it is nonfunctional, and fails to achieve its aim. What makes something beautiful is not strictly simplicity, symmetry, complexity, or any other such characteristic. Instead, what makes something beautiful is that its characteristics are all appropriate to its purpose. Complexity can be exceedingly beautiful, as long as it's not gratuitous complexity, which is just chaos and confusion. Likewise, simplicity can be exceedingly beautiful, but if you make something gratuitously simple, you get dullness rather than beauty. Gratuitous simplicity is merely boring.
When you're writing source code, make it elegant. When you've written something, go back and look it over, and for each and every thing you've done you should take a moment to question whether it's really necessary, or even functionally desirable, to have it in there. You probably won't get it perfect, but you can at least make it awfully pretty, which is a good thing as long as you do so by addressing elegance rather than trying to disguise the inelegance of your code by conforming to formatting conventions without rethinking your program logic at all. Refactoring, in the end, is really just about looking with fresh eyes for any opportunities to introduce elegance by removing the gratuitous.
If you're unlucky, you may discover that making your code significantly more elegant might require rewriting it in a different language.
The following definitions are from Princeton WordNet:
elegant (adj.): of seemingly effortless beauty in form or proportion
gratuitous (adj.): unnecessary and unwarranted