Part of the lure of the group ride is the friendly (or sometimes not so friendly) competition. Many groups have taken on the racing convention of having marked places along the route for sprint or KOM (King of the Mountain) points.
KOMs are, by definition, at the top of significant climbs. Generally points are awarded for the “category” of the climb, which is determined not only by the steepness and length of the climb, but also where in the route the climb falls. For example, if two climbs follow one right after the other, but are otherwise identical, it may be that the second climb is of a higher category, and thus worth more points.
Sprint points are a little easier to deal with. There’s a line, and the first person to cross it takes the point. Sprint points can also be a little more dynamic and exciting – at least in my opinion. As the group approaches a sprint point, folks will begin to jockey for position within the group, trying to place themselves best. The idea here is to hold of on starting the sprint until just the right time – optimizing the potential to get out in front before your fellow competitors can answer your challenge.