To invoke means to call on something or someone for help, support, or authority. When a wizard in a story invokes ancient magic, she's summoning its power to use. When a lawyer invokes the Fifth Amendment, he's calling on that constitutional right to protect himself.

A speaker might invoke the memory of a historical figure to strengthen her argument. A student council president might invoke the school rules to settle a dispute. When a religious leader invokes a blessing, he's calling on divine power.

You can invoke ideas, laws, names, spirits, memories, or rights. The word suggests something more formal and deliberate than just mentioning something casually. If you simply mention recess rules during an argument, that's one thing. But if you invoke those rules with authority to end a disagreement, you're calling on their power to settle the matter. When you invoke something, you're bringing its full weight and authority into the situation at hand, actively using that authority to accomplish something.