To be more specific, the beam expander improves the divergence. With a normal 3 element or single element lens the beam will expand more rapidly, more so with a single element than a 3 element. With the beam expander the beam starts out larger in diameter but doesn't expand as rapidly, even though there is a power loss from the additional optics, at some distance it will outperform the lens by itself. I remember a long time ago someone here shined a green laser at a hillside multiple miles away and his friends were there to take a photo and measure the diameter of the beam and it was about 10 feet, and there was someone else here that said they shined their laser at a sign on the other side of a lake that I think was a mile accross while their friend measured the beam at about 3 feet I think it was. If these people could have used a beam expander then the beam would have been smaller at those distances. If you take 2 identical lasers one with a beam expander and one without, at some distance the one with the expander will begin to outperform the one without the expander. So most of us probably don't need an expander for anything, but if you want to put a dot on something far enough away then you need the expander.
Alan