Wisdom describes a character's willpower, common sense, perception, and intuition, whereas Intelligence represents the ability to analyze information. An "absent-minded professor" has low Wisdom and high Intelligence. A simpleton with low Intelligence might nevertheless be very perceptive (if he has high Wisdom). The wise character is capable of intuitively understanding others, occasionally having insights into their motivations.
Some of the things which a character's Wisdom score affects are:
Will Saving Throws- A character adds their Wisdom bonus to Will saving throws, used to avoid the effects of spells such as charm person.
Divine Spellcasting- Several divine classes use Wisdom for their spellcasting. Clerics, Druids, Paladins, Rangers and Spirit Shamans must have a Wisdom score of 10 + the spell's level to cast a spell of a given level. For example, a Spirit Shaman would need a Wisdom score of 15 to learn a 5th level spell. Additionally, Clerics, Druids, Paladins, Rangers and Favored Souls use Wisdom to determine the Difficulty Class (DC) of their spells.
Monk Abilities- A Monk's Wisdom score is used to modify many of her class abilities. For instance, when unarmored and unencumbered, a Monk may add her Wisdom bonus to her Armor Class. As such, Wisdom is a very important attribute for Monks.
Wisdom is important for Clerics, Druids, Paladins, Rangers, Spirit Shamans, Favored Souls, and Monks.