The clause is really a state's rights clause. A state may not pass a law that makes something illegal that was legal before the law was passed. In other words if a state suddenly passed a law that said it is no longer legal to park your car in front of any government building, but it was legal to do so yesterday, the police cannot come to your door and issue a ticket for parking in front of a government building because you did it yesterday.
The constitution actually uses the phrase ex post facto law in Article 1 Section 10 Clause 1.