When you adduce something, you offer proof in support of an argument. If you’re trying to prove that you didn’t eat the last cookie, you might adduce the fact that your dog’s mouth is covered in cookie crumbs.
The word adduce comes from the Latin adducere, which means "to lead or bring along." If you were a lawyer, you might adduce, or bring forth, a witness in order to help your case. You might also adduce a piece of evidence, like a fact, to help with your argument. You might think of the word add to help you remember the definition of adduce: when you adduce something, you are adding to an argument by offering proof.