If you act with caution, it means you are careful. Be sure to use caution when walking across a patch of ice. Otherwise, you might end up sprawling face-first on the ground. Ouch!
The noun caution can be used to describe something that calls for careful action and the need to avoid risk, such as a volatile political situation that requires extreme caution. The word also has a verb form with a similar meaning. It’s a more formal way of saying “warn” and usually appears with against or that, as in, "Teachers caution against waiting until the last minute to study," or, "They caution that effective studying takes a long time."