Do I have to reveal a card, for example, a Shoggoth or something, and say I’m afraid of it?

A: In this case “reveal” means “confess to your friends”. For example, if you are someone who is afraid of spiders, or nuclear war, or whatever, then you can say, “I’m afraid of spiders,” or “I fear nuclear war,” or whatever, and draw a card for revealing this secret about yourself.

Other players may later use this info against you!