IVs (individual values), also called DVs (deter[minate] values), are simply technical terms for your Pokemon's genes. When a Pokemon is encountered in the wild (and, subsequently, caught) it has a random number (0-15 in RBYGSC; 0-31 in RSFL) rolled for each of its stats (except HP, whose DV is derived from the others, at least in RBYGSC). This number is permanent and cannot be changed in any way without RAM modification (IE, GameShark). These DVs determine how high or low that Pokemon's stats can possibly go; if the Pokemon has a DV of 15 in defense, it will be able to achieve the maximum possible defense for its species. A DV of 0 will result in the minimum possible for the species-- not too good. A DV of 7 or 8 will be "average." The best way to find a Pokemon's DVs is to catch it and ensure that it receives no stat experience/effort points whatsoever, level it up to 50 or 100 (the easiest levels to check with, not necessary, but much more reliable-- Pokemon rarely show stat variations among the same species at lower levels) with rare candy, and find one of the numerous DV-checking utiliities on the web.
Note that in GSC, special attack and special defense run off the same DV. In RSFL, SA and SD have separate DVs.
In a nutshell, high DVs means high stats. Don't sweat trying to find a Pokemon with high DVs in a useless stat for that Pokemon (IE, a high attack DV for a Pokemon with low attack and high special). The chances of finding a five-way max Pokemon in RBYGSC (in fact, the chances of any combination of five specific DVs) are 1:16^5, or 1:1,048,576: one in a million, as it were. A more realistic approach is trying for only two (1:256 odds) or three (1:4096 odds) specific DVs. These odds are obscene in RSFL (a six-way max is 1/32^6, or 1:1,073,741,824-- one in a billion), so getting good DVs is considerably more difficult in those games.
Aside from stats, DVs also determine shiny Pokemon, the type and power of Hidden Power, and Mirage Island, which I've heard about three different theories for, but I can't test them yet.
I think I had something else to say on the subject, but something took my concentration so I lost my rambling tempo and forgot. More later if I remember or someone reminds me, I guess.
