It's a subtle matter of relative factors, the same ones that govern any component's effectiveness or quality.
When considering wheel quality, four or five chief characteristics come to mind off the top of my head: weight, durability, rotational stiffness or responsiveness, ride quality, and aerodynamics (the least relevant of the lot for most folks, generally). Weight is an obvious and popular consideration -- less weight, in general, means less to haul up a hill and less to spring forward from a standstill. The lightest clincher wheelsets hover around 1000 grams for the pair; heavier sets straddle the 2000 gram mark. Most retail wheelsets ranging from $400USD/pair to $1500USD/pair fill the 1300g to 1600g zone.
Durability is another no-brainer, although its less intuitive than weight when it comes to price. Many of the sexier and pricier wheelsets are positioned as race-day wheels; they're light and marvelous, but not beefy enough for every day or training use. The cheapest wheels suffer the same fate by virtue of being junk. Look for middle-ground... the uber-popular Mavic Ksyrium SL owes much of its commerical success to the notion that it's remarkably durable for a high-performance race wheel, and fit for frequent use. Plenty of much cheaper wheels offer the same benefit, though; Velomax is a great company with durable, inexpensive options; Campy's mid and lower-end wheels have big followings as well. The Ksyrium's little brother, the Ksyrium Elite, is cheaper and supposedly tough as nails.
Fancy wheels boast flex-free responsiveness as well -- that quality of rolling with precise power transfer when you stomp the pedals at a red light or accelerate aggressively. This is an elusive quality, though, because a wheel which is super stiff in this sense may not a) be the lightest, or b) be very comfy to ride. Many regard the Ksyrium SL, for example, as a snappy, jump-from-the-gun wheel with a harsh soul.
Finally, aerodynamics come into play, though not for most folks in most situations. A deeper, sexy rim extending beyond the 32mm or 35mm mark starts to offer a subtle aerodynamic advantage when traveling at speeds in excess of 20 or 25mph. Unless you're spending over $1000USD, though, that extra rim material tends to come at a significant weight penalty, and cheap or pricey, can cause issues in cross-winds. Unless you specialize in time-trial or triathalon-style courses, with stretches of pure speed unhindered by climbs or other trouble, you're better off keeping aerodynamics low on your priority list.
There's no doubt that a wheel upgrade can confer some advantage to a racer, but these qualities are all relative -- it comes down to how little a benefit you're willing to buy for how much cash. A good wheel can make your bike a great deal more fun, for a cost. What's your budget?
