Rating is how the game determines the rank of the deck you submit to the arena (the one with bonuses, like double draw, more marks, extra HP, and upgrades).
For each win it gains a certain number of points (depending on the arena), and higher points gives a better rank (as well as a few
). Losses deduct points. If your deck ranks a higher number than 500, then it won't be played anymore until you make a new deck. A new deck has a rating of 0, and a rank of somewhere around 250. In addition, if your deck wins, then that's when the thumb voting comes into play, which adds or deducts rating points also.
Also, older decks are weaker because they lose HP every day, and you lose more HP in your deck per day as it gets older.
I also think it would be awesome to see the thumb history of your deck.