Google's AI describes it better than I can: "A projection matrix is a square matrix in linear algebra that, when multiplied with a vector, outputs the projection of that vector onto a specific subspace; essentially, it "flattens" the vector onto a lower-dimensional space while maintaining its relative position within that subspace."
I use perspective projection matrices for all things 3D in my voxel engine (calculations of ray origins and directions, rasterized lines and triangles). Rasterizing pipelines in 3D graphics use the matrices to flatten projected 3D coordinates onto 2D screen space coordinates in order to rasterize in 2D.