I can only think of two functions that would make any sense as far as the actual plots of the books. The first is that, like in Quidditch, there’s at least one player with a “Seeker” aspect to his or her role, and capturing the Snitch is worth sixty billion points if he or she manages to get it. Harry and Draco, I think, were the two main Seekers in the books. I supposed initially that this might be a decent third party win condition.
The other is that the Snitch was the thing they handed out to all the contestants in Goblet of Fire, and that Harry had to unlock to hear a message about one of the feats in the tournament, so there’s a precedent for it being a mechanism to pass secret information along. I was hoping for this one, obviously, but it looks like that isn’t what it does.
I just thought of a third one - and, uh, spoiler alert, I guess. At the end of the last book, Harry’s carrying the Snitch that does the “I open at the close” thing. It lets him talk to dead people once he’s ready to go down to the forest and. You know. Go down. (Hey, that’s what happened to HardlySanguine!) Maybe the Snitch does something if you die when you’ve had it the previous day.