Provisionally, PSR is the view that any contingent ('contingent upon..' == dependent) truth has a sufficient reason.
The reason why we assume this is true is because if something is contingent upon something else, then there must be a reason for it's outcome – i.e. at least, the very thing it is contingent upon.
An example was given,
The first statement is a necessary truth because denying it (ex. as with the second statement) results in a contradiction. Cats are, by definition, mammals, so saying that they are reptiles is a contradiction.
The third statement is a contingent truth because it is possible that cats could have evolved without claws.
This is similar to the distinction between essential and accidental qualities. Being a mammal is part of a cat's essence, but having claws is an accident. (Note: This is a terrible argument because being a cat does in fact entail having claws. A better example would be perhaps snakes which are or are not poisonous).