It shows to a player his own performance compared to other players playing the same champion in the same role.
The score you get depends on some metrics, but they aren't discussed in detail:
It’s based on the champion and role that you just played in a game. So, for example, we look at Annie mid differently to Annie support. We take a series of performance metrics and compare how you do to all other players in your region in your champion / position combination. It is percentile driven - so earning a high score means you performed in the top x% of players on that champ in that position. The grade itself governs the point gains.
top x% of players" determined by comparing performance of all players irrelevant of their ELO?
In other words, when a silver player scores S+ does that mean that he performed as well as a diamond player?
(If that is the case, my guess is that S+ in lower ELO should be rather rare excluding smurfs. Do you see this happening in low ELO?)
Or does a player get compared with roughly same ELO players when determining his score?