People often think postulating a bounded universe (such as that which is widely believed we inhabit) is itself enough to solve Olbers' paradox. This is not so.

A bounded universe involves "no boundary conditions". This is a technical term which means just that -- no point of the universe is any closer to its "edge" (the universe has no edge). To help visualise this, consider the surface of the Earth. It is bounded, but all points are equivalent; none is closer than any other to the "boundary".

One way to simplify a bounded universe with the no boundary condition boundary condition is to consider a torus: a universe shaped like a large cube, with the rule that moving "out" through one side means moving "in" through the opposite side (players of Asteroids and PACMAN will be very familiar with this universe). Now fill the "universe" with a few stars. Then it is true that you will see a star, no matter where you look (note that you might be seeing a nearby star which has "wrapped around" several times; its brightness will be diminished accordingly). And you might as well be in an infinite universe, with stars distributed in a regular fashion; Olbers' paradox still works.

Now, you could talk about a finite amount of matter in an infinite universe. But this imposes the idea of the existence of "the center of the universe" in your Physics; this is not a good idea...