If you look at the equation there you can see that the wave function depends on the coordinates of all electrons, so its a 3N dimensional problem. So you need to know all the coordinates of all the N electrons. If you look at the electron density, it doesn't depend on the coordinates of all electrons. The vector r "shows one position in space" where you can define the concrete electron density at that position. So it's a (usually) 3 dimensional problem. You don't need to know all positions of all electrons anymore, because you're just looking at the electron density, which kind of means "how many electrons will be on average in that position". And you can actually measure the electron desity with STM, so at a certain position you have a certain electron density and it changes if you change the coordinates of the observed position. And point charge means that you have an electric charge that is considered to exist at a single point, and thus having neither area nor volume. So for instance the charge is not smeared over an area, but is just at a single point. Hope it was understandable and right and hope that it helped :)