The adjective wise describes someone who has experience and a deep understanding. Your wise older sister always gives the best advice.
When you make a decision based on careful thought and good judgment, you've made a wise choice. If someone calls you a wise guy, though, it's not a compliment: it's likely to be a criticism of your joke at someone else's expense or your rudeness. To wise off (or sometimes, to be wise), has a similar meaning: to talk back or be disrespectful.