Rating tells me:
- The likely skill of the opponent.
- Which section of a tournament I get to play in.
- In a club match, who plays which board
- Whether I appear to be improving or not.
There are all sorts of traps with rating. One player in my last club achieved a rating above his skill by regularly getting into complicated middlegame positions against better opponents, and offering a draw. The next year, his opponents caught on, and his rating fell. I have won (and almost certainly lost!) games due to an opponent playing against rating number, and not the position.
But there is an indication of skill. The comment about with whom you get interesting games is a good way of putting it. Michael de la Maza (Rapid Chess Improvement) suggested max 200 points above your grade, which seems fair. Against a much better or worse player, you are likely to be outplayed/outplay your opponent in most stages of the game.
The last point helps motivation a bit. If I am getting better, it is good to know. If not, I need to think about why: Do I need to look at some aspect of my game? Have I just got too many other things on my mind? Or should I concentrate on *my* game while playing, and not look at others in the tournament hall? Or do I just need to play more with the new opening I have just started with?