The points are what increases your user level, so you can post more questions and answers per YA day (Levels 1 - 4). From level 4 - 6 there is no benefit to gaining points, but once you reach Level 7 (25,000 pts or more) you also gain the ability to relocate misplaced questions to more appropriate subcategories (although far too many Levle 7s do the opposite).
The points were to encourage participation in the site, since there are many people who will simply try to see how many points they can get (much like playing a game for points...the points mean nothing, but it's human nature to keep playing to try to beat your previous best score).
Not to mention, many would be here even without the points, because there can be interesting questions and informative answers (not as many as in years past, but they do exist) and it can be an interesting/enjoyable way to pass the time. Most of the time I spend here is while I'm at work, because my job doesn't often keep me very busy (and I've seen others post similar, over the years).