Effort Values for the EV-intimidated
First, a note: this isn't how it works in Gen 1 or 2, and in Gen 6 it is easier to do Super Training than get EVs from wild Pokémon (though the underlying mechanics are the same). For Gen 3, 4, and 5, however, read on!
Every Pokémon's stats are based on four things: their species' base stats, their nature, their Individual Values (IVs) and their Effort Values (EVs).
Base Stats are pretty easy to understand. They are why even very fast Shuckle are slow and very slow Ninjask are fast. (For that matter, the very fastest Shuckle, at level 100, is slower than the very slowest Sandslash at level 100 and the very slowest Ninjask at level 40.)
Natures are pretty easy too, once you remember that in-game, red is better and blue is worse. (If it helps, remember that in battle, stat-up moves produce a red effect and stat-down moves produce a blue one.)
Individual Values are assigned when a Pokémon first enters a party - whether as an egg or when it's caught in the wild or in Entree Forest. They do not subtract from base stats, and at most add 31 additional points to a stat at level 100. (It is possible to have 31 in every stat, or 0 in every stat.) At level 50, therefore, they only add at most 15 points; at level 20, they only add at most 6 points. This means that for anything other than battling human opponents who care about IVs, they can safely be ignored.
That brings us to Effort Values. The games tell us that a Pokémon who levels up through battle is stronger than one who's leveled up in the Daycare or via Rare Candy. This is true up to a point:( Simplest explanation: you can only get so many EVs. )
( There are ways other than battle to get EVs. )
( a little bit of math )
Executive summary: You can only get so many EVs, whether through battle, Vitamins, or Super Training. If you use Super Training in Gen 6 effectively enough, you can be Fully-Trained at level 1: at that point you could put it in the Daycare for 99 levels and it would be no weaker than if you'd battled from 1 to 100. In Gen 3, 4, and 5, getting full EVs will involve at least some battles (and thus some exp), but after that point, it doesn't matter how they get the experience.