Strict describes someone who sticks to a particular set of rules. If your math teacher is strict, it means that she expects her rules to be followed to the letter.
The adjective strict always has to do with rules. Your strict parents enforced rules and expected you to obey them. Your cousin might be a strict vegetarian who always follows her own rules about what to eat. Strict laws demand to be followed, and a strict follower of the First Amendment supports free speech no matter what. The Latin root of strict is strictus, which means "drawn together, tight, or rigid." A rigid adherence to rules is exactly what makes someone strict.