Pappus' and Desargues' theorems are two notable theorems in projective/affine geometry.
I am trying to understand their relevance and significance in the context of (projective) geometry. Specifically, I fail to see the big picture: what is so important about a certain number of straight lines intersecting at a certain number of points?
I would appreciate some intuitive explanation and a broader context in which these theorems are as important as, e.g., Pythagorean theorem in Euclidean geometry.