Just What Is “A Priori” Justification?

What is your justification in believing that 2 + 2 = 4? You are justified because you understand the concepts involved. You understand what all the terms in that simple sum mean and that, as a result, the sum of two and two is four. Philosophers call that sort of justification a priori justification, and describe it as justification independent of experience. But how could there be such justification? Isn’t all justification dependent on experience?