Someone who is worldly-wise knows how life and people really work. They have been around, seen how deals get made and how people lie, and so they are hard to shock and hard to fool. If a stranger offers them something too good, they smell it straight away.

Two pieces of the meaning matter equally. One is knowledge — of money, of cities, of how people behave when nobody is watching. The other is protection — that knowledge keeps them safe. So it is usually a compliment, or at least a respectful description: "her worldly-wise aunt", "a worldly-wise old shopkeeper". Its opposite is naive, innocent, or green.

The word feels a bit literary and slightly old-fashioned; it turns up in novels more than in conversation. It is very often used about older people, and often about someone who did not get this wisdom from school. There can be a faint shadow in it too — the suggestion that this person has lost some innocence to gain the knowledge, and may be a little too comfortable with how ugly the world is. The sentence decides how much of that shadow you hear.

Note that *worldly* on its own is a different word — it can mean concerned with money and possessions rather than the spirit. Worldly-wise is not about being greedy; it is about being hard to trick.