From what I understand, it determines how regularly a player plays true to their ratings..... I think.
I don't have the actual ratings to hand, but if we use Peyton Manning and Andy Dalton as examples.
With Peyton being a 5 star in consistency, he will almost always play with his passing ratings at say... 90, 94, 90 (SAC,MAC,DAC)
While Andy Dalton has 1 star consistency, so even though his ratings might say something like... 85, 75, 70, his ratings have a higher chance of dropping in a game as he is much less consistent. So you are more likely to come across games where he throws very poorly.
I could be completely wrong though. Nobody really knows when it comes to the logic behind EA's work...