Of the six stats, Wisdom is actually one of the more-slippery ones. It represents, at once, one's willpower and inner fortitude, one's common sense and perceptiveness, and a variety of other instinctual mental traits that are neither associated with reason (and therefore Intelligence) or personal magnetism (which is Charisma). Skills associated with it include Perception, and the Notice, Spot, and Listen tests that got collapsed into it, Insight/Sense Motive, Medicine, and Survival, as well as most forms of mental defense.
Wisdom is perhaps the best-designed sort of stat: it has a variety of uses (Perception/Spot in particular is often cited as the most important skill in the game, and Sense Motive is almost as important for any social character), and its role in bolstering mental defense means there are very real consequences for any character who drops it down too far. Yet, at the same time, like Constitution, its role in combat is largely secondary, so no one wants to focus on it exclusively either unless they're a spellcaster that relies on it for their powers. Thus, it usually sits at a happy medium. It contributes a lot, without contributing so much that anyone that drops it too low is gimping their character beyond the point of use.
Wisdom is one of the three "mental" stats of D&D and is used as a power source for two kinds of spellcasters. Unlike the inner power of a Charisma-based caster, though, or the rigorously logical mind of an Intelligence-based caster, Wisdom based casters tend to channel the power of other sources. Most-notably, this category includes both clerics and priests, whose Wisdom helps them to connect with divine powers, and druids and rangers, who can connect with nature in the same way.
Wisdom is important for clerics, druids, and rangers, all of whom use it cast spells, as well as for paladins in editions in which they also cast with it, rather than the Charisma that fuels all their other class powers. Monks typically gain a bonus to their Armor Class for having high Wisdom as well, and the rogue needs at least a decent score in the stat to be able to properly scout ahead for traps, ambushes, hidden doors and treasure caches, and other such things. But, again, since Wisdom offers many benefits, it, like Constitution, is an extremely popular secondary stat even for classes that don't derive direct benefits from it.