There are fundamentally two forms of balance: PC versus PC, and PC versus World. They serve very distinct purposes.
PC versus PC:This type of balance exists to ensure that every PC gets a roughly equal share of the spotlight*. It applies to class abilities, magic items intended for PC use, feats, henchmen, XP, etc. These elements may be thrown together or split out into silos; see the bit on scope below.
PC versus World: This type of balance exists to inform the DM's assessment of how tough an obstacle is, both in absolute terms and relative to the PCs. It applies to monsters, traps, and skill challenges or equivalent. This information may be used a) to award experience, and b) to design suitable adventures for a given party.
In addition, there is the question of scope. Balance can be viewed as a literal balancing act, where you put (for instance) a bunch of fighter abilities in one pan of a scale, and a bunch of wizard abilities in the other, and see how the scale hangs. Scope is the question, "How much stuff are we putting in each pan?"
AD&D had a very broad scope, throwing the entire campaign's worth of fighter abilities in one pan and the entire campaign's worth of wizard abilities in the other. Thus, the fighter was stronger than the wizard at low levels but weaker at high levels, and this was seen to balance out because the scope included all levels. Likewise, noncombat utility and combat utility all got thrown together.
4E, on the other hand, had extremely narrow scope. Classic 4E had the narrowest scope of any edition: You took the combat abilities of the fighter in a single encounter at a given level, and weighed them against the combat abilities of the wizard in a single encounter at the same level. Essentials broadened the scope from "encounter" to "day," but it was still very tight.
Broad scope allows for maximum flexibility in class design, but carries the risk that any given campaign may include only a fraction of the scope in question. If your AD&D game wrapped up at level 6, the fighter would never get the "weak levels" to counteract the strong. Moreover, an overly broad scope can exceed the players' attention span. Many players don't feel that six months of frustration followed by six months as king of the hill, or vice versa, is a fun way to play.
Narrow scope ensures that balance applies everywhere, but places heavy constraints on design. Classic 4E demonstrated this with its rigid AEDU structure, which many players felt was stifling and boring.
[SIZE=-2]*D&D game balance does not generally concern itself with actual PC-on-PC combat. The fighter and wizard are assumed to be on the same side, so it doesn't matter which of them would smoke the other in a duel.
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