Barycentric coordinate system is a way of locating a point in space. It is like a set of coordinates that tells you where that point is. Imagine an area with three fixed points: A, B and C. If you want to locate another point X, you need to use the barycentric coordinate system. This means you will pick three numbers (x, y and z) which add up to 1 and use them to calculate where the point X is. These three numbers (x, y, and z) tell you how much of each fixed point - A, B and C - X is made up of. So if one number is 0.3, then X is made up of 30% of A and the other numbers tell you how much of B and C X is made up of. This way you can locate your point X anywhere in the space between A, B and C.