Many believe that there are two types of knowledge
: a priori, and a posteriori.
Think of the difference between knowing the two following facts:
1. 2 + 2 = 4
2. The sun is big and yellow.
You know both to be true - they are both knowledge. The difference between them is the diference between a priori and a posteriori knowledge...
2 + 2 = 4 can be said to be true without reference to the outside world. I can know that 2 + 2 = 4 without having to see 2 apples and 2 oranges in my fruit bowl totalling 4 fruit. This is a priori - you know it's true without having to see it in the world - ie, you know it without prior experience.
You only know that the sun is big and yellow because you have seen it (that it's yellow), and that you've been told that it's big. If you had never seen the sun, you'd not know that it was big or yellow. For you to know its size and color, you have to refer to the world. This makes it a posteriori - you only know it based on experience.
Why it this important? Primarily in science: when performing research, clear distinctions need to be made between the two types of knowledge. All a priori knowledge (eg, maths) can be taken for granted, whilst all a posteriori knowledge (eg, observation) must be proved.
You may feel the disinction is simple, but consider medical ethics. Perhaps abortion - some would consider abortion wrong a priori (eg, it is wrong because God says so) , some might consider it acceptable a priori, whilst wrong a posteriori (eg, it is wrong because it is painful to the inoccent foetus). In this case, our belief (that abortion is wrong) is the same, but with the fundamental a priori, a posteriori disinction.