Representing points in a homogeneous way on a projective plane is done for easier way to write down a coordinate system of a point in infinity, and also it’s very convenient way forming lines from points in algebric formulation.
Viewing a point on an image from a distance(1 distance away (0,0,1)) from the (origin (0,0,0) ), so the point is no longer a point, it’s a ray from the origin to the point and extends to the world.
A line in an image corresponds to ax +by +cz = 0 (in vector notation 0 = [a b c]Transpose[x y z]) in projective space.
