Everything is based on mind, is led by mind, is fashioned by mind. If you speak and act with a polluted mind, suffering will follow you, as the wheels of the oxcart follow the footsteps of the ox. Everything is based on mind, is led by mind, is fashioned by mind. If you speak and act with a pure mind, happiness will follow you, as a shadow clings to a form.
-Buddha
Wisdom is often confused with intelligence, because the two are usually found together in world figures. In Dungeons and Dragons, they have no bearing on one another. Wisdom measures a person’s judgement, common sense, accumulated knowledge, and levelheadedness. Wisdom contributes to a lot of skills, and also determines your character’s will defense (their ability to resist mind-affecting spells or abilities like illusion and enchantment).
8…
...is below average. You’re impulsive, reckless, and perpetually out of your element. You have no head for history, or for subtleties of the world around you. With 8 wisdom, you’re blind to subtext. Kind of like Michelangelo, of the Teenage Mutant Ninja Turtles.
10…
...is considered average. Certainly some things get past you, but you’re as wise as anyone else. Ron Weasley has 10 wisdom; it isn’t anything remarkable.
12…
...is above average. You know what’s up, and some people look to you for advice. You know how to weigh the pros and cons of a situation before making a decision, and you usually feel good about the decision in retrospect. Spiderman’s Uncle Ben has 12 wisdom; just enough to come up with a snazzy line about power and responsibility.
14…
...is impressive. A lot of world leaders (or the people who advise them) should be up here. They aren't, because politics tends to value unscrupulousness over morality, but they should be. You’re well traveled, and generally know the best course of action for a given situation. You can tell when somebody is lying more often than not, and people look to you for advice.
16…
...is among the top 5% or so. Gandhi. Martin Luther King. Rafiki (Lion King). You know a lot about a lot. At this point, think about your wisdom as you role play. Your character should probably have a moral compass or ideology of some kind that you are working toward; what you say, how you act, should reflect that.
18…
...you’re a paragon of wisdom. When you open your mouth, people around you are inspired and awestruck. Yoda, Jesus, and Buddha had 18 wisdom. (I’m going with an all-or-nothing viewpoint on whether they existed, because I really want to live in the same universe as Yoda) You are a font of wisdom, so that should definitely be reflected in how you role-play. Choose your words carefully, and try not to be too impulsive.
Wisdom is a great governing point on how your character should react to situations, but ultimately it is up to the player. Even characters with a high wisdom can make mistakes (many of my paragon examples were assassinated, and the other agreed to train Darth Vader) and that has no bearing on their overall wisdom. In my opinion, these mistakes come out in role-playing the same way that a high dexterity character can trip when they roll a 1.
It's important to remember that Wisdom is not the same as education. Wisdom represents your character's life experience and judgement. The healer in a barbarian tribe could be wise and illiterate, the same way that a power-hungry young wizard could be learned and unwise. Wisdom isn't about what you know (most wise characters have gained their wisdom through study/meditation as well as experience) so much as how you act.