The number of points indicates the number of pointy parts on the antlers. The more points roughly scales with the age/health/size of the deer, although smaller deer can have larger antlers depending on nutrition and genetics.
In our area, we generally expect whitetail bucks to grow as follows:
Yearling - "Button Buck", meaning a fawn buck with only small bumps on his head, no visible antlers. Or, a "spike" which means two antlers with no branches.
Second year - "Fork", indicating a four point, or maybe a six point.
Third year - 8+. Coming into his prime.
This can vary by quite a bit geographically, primarily due to food sources and climate. Harsh winters can kill off a lot of deer.
Most deer taken are in the yearling - second year range, although it is considered bad form to shoot a yearling, especially a button buck. So, shooting an 8 point generally means more meat but also that you have taken a more wary, wily animal, who was probably having a weak moment while chasing a doe, but nevertheless indicates that you are a good hunter, or really lucky.
Aside from that there are also at least two scoring systems that will assign a number of points to antlers based upon length, girth and the number of points. Books are kept on that shit and I know vaguely how it works but I've never had much interest in it.
TLDR; Points = penis size of the hunter but does are tasty too.