To invoke is to call up something such as a law, a higher power, or even a ghost. In court, you might invoke the Fifth Amendment (the right not to say something that will make you look bad) if you don't want to talk.
You can invoke all kinds of people or ideas, alive or dead: "She invokes the spirit of good writing when she proofreads her work." In a time of need, you might invoke a higher power. You could invoke Martin Luther King when talking about equal rights. You might even invoke the spirit of your dead cat at a séance. Just make sure you don't evoke (to bring on a strong emotional reaction) your dead cat; that would just be weird.