A priori and a posteriori are terms used when talking about the process of reasoning.
A priori means 'before experience' and is used to describe reasoning that is done without any experience or knowledge of a situation. For example, if someone says, "All cats meow" without ever hearing a cat meow, this is a priori reasoning.
A posteriori means 'after experience' and is used to describe reasoning that is done after gaining experience or knowledge of a situation. For example, if someone says, "I have heard cats meow", this is a posteriori reasoning because they have gained the experience of hearing a cat meow.