Chief: I got one!
C.M.O.: I got one too!
Tivk: I am successful as well.
Nok: There are some more moving to the left!
Tivk: On closer inspection I got a rock.
Mukh: Okay that's ... six we got. That's the legal limit. We can take them back to my clan holdings now.
Chief: There's going to be a hell of a fish fry.
Mukh: ... what?
Chief: What'd I say?
Mukh: Give me that net please. Thank you. See you back at the clan holding.
Chief: What'd I say?!
C.M.O.: Chief. These are the immature form of Mukh's species. They lay their eggs out here and come back after hatching season starts to capture their quota of young for their family.
Chief: I guess I brought that cooler full 'a brews for nothing.
Nok: I think you'll need every beer.
Tivk: Begin imbibing now. We have experience with angry mobs.
Wisdom is usually regarded as instinct, perception, understanding your own ways of thinking and the way others think. It is often used to measure psionic potential if your game includes that. This applies mainly to humans of course. Other species may have a very different idea of what makes a being wise although generally speaking wisdom is something that increases with life experience.
Wisdom often gives a bonus to experience points earned or bonuses to psionic powers and abilities. In a robot or synthetic it can represent how well the AI can learn from its experiences.
A robot or synthetic might use its Intelligence to give bonuses to its equivalent of psionics to represent hacking ability.
Wisdom might also be a criteria for a being to exceed level limits (if you're using them). Since Wisdom tends to increase with age this can explain all those extremely high level and multi-classed NPCs who seem more capable than other PC members of their species or product line.
Wisdom can also give a bonus to attempts to contact or communicate with newly discovered species. While Charisma or force of personality works dealing with beings you understand, Wisdom is what helps you understand them in the first place.
A high Wisdom could be used to allow aliens to perceive special things that humans can't. A being from a planet that undergoes numerous quakes could develop a sense for seismic activity based on Wisdom or a being from a world orbiting a flare star might be able to detect radiation storms from environmental or physiological clues others would miss. Some might even have a chance to detect secret doors on a 2 in 6 chance.
Wisdom could be used in place of Charisma if your values age and experience. Your mystical order of knights might not care if you're particularly friendly if you have command of your thoughts and feelings and see into the hearts of others.
Wisdom could be used in place of Dexterity to modify your armor class to represent precognitive ability or a combat sense. Using it to replace Strength or Constitution is harder to justify, but it could represent control of your endocrine system allowing you to trigger adrenal surges or respond more efficiently to disease and toxins.
Using other characteristics for Wisdom is harder to explain perhaps because a central bias of our culture is that there is no substitute for experience. A race of adept beings might be able to copy movements and abilities from those around them. These mimics could get the experience bonus for their Dexterity or Intelligence. Likewise a crude brawler type might not get an experience bonus for being insightful and perceptive and be more likely to succeed and improve due to high Strength or Constitution letting him rebound from beatings quicker and put what he learned to good use.
Mukh: Accepted. On both counts. I'm glad you learned something from this.
Chief: I guess you can teach an old dog new tricks.
Mukh: ... that isn't a euphemism for telling me to go f...
Chief: No! It means ... I learned something from all this and in spite of often being a stubborn old gyrene.
Mukh: That's the good thing about being egg layers and coming into the world non-sentient and feral. None of us know exactly where we come from so we really don't get hung up on it. We think it's more important where you are and where you're going.
Mukh: Where in Throgg's name did you get the idea this was a hunting trip?
Chief: ... Nok told me.
Nok: You bastard!!
Mukh: Why you .... REEEEEEEEE!!!
Chief: Two down and one to go. No one messes with the Chief.