The forum seems to receive a bunch of enquiries on this subject on daily basis, so to explain and to answer some of it, I've explained things briefly here and compiled a brief FAQ in the end to answer the most common questions people seem to have about the rating system.


Basics

The rating system is threefold. The two more obvious parts of the system are your personal rating (PR) and your team rating (TR) that represent the de facto rankings. They exist to rank your team, in addition to providing grounds for arena rewards (rating requirements for weapons, and so forth). You can view these ratings on your team screen. The reason why PR and TR both exist and are separated is trivial: the team rating makes it possible to rank the team on the battleground's ladder, and the personal rating makes it difficult to abuse the system to purchase gear (ie. attend a team for a short period to be on the TR to obtain gear is not possible because your PR will not be high enough, hence purchasing gear rewards requires both personal and team rating.) The rating change you are given on the sheet that is displayed at the end of the match concerns your team rating. Personal rating, if different from team rating, tends to slowly move towards team rating - or vice versa, over games played.


MMR

This part of the rating system inflicts considerable amounts of misunderstanding and confusion upon players. It's the funny figure you're also shown on the end of the game chart. It changes when you win and lose games, but to confuse you more, the changes aren't displayed on the end match sheet. Now, the idea of matchmaking rating, MMR, is to pit you against teams of roughly equal skill level. Hence, over a period of games, MMR will tend to anchor itself on a level which represents the rough skill level you play on - this will generally indicate a TR/PR level also. For example, if you feel stuck at around 1200-1300 TR/PR/MMR, the most likely cause for this is because you're playing roughly 50-50 wins and losses against teams on that MMR range.

Worry not, though, matchmaking rating is not something that condemns you into a specific rating range forever. By beating opponents, your MMR increases. If you beat opponents vastly above your MMR, your MMR increases more - and the opposite happens if you lose to lesser opponents. The more your MMR is above (or below) your TR, the higher the gains (or losses) will be should you win (lose) games. In brief, if your TR is 900, and your MMR is 2000, beating a game can net you 42 TR, while losing can net you 0 TR (however, both losing and winning will affect your MMR). The easiest way to understand MMR is to perceive it as an anchor towards which your TR/PR tend to move to: you can improve your MMR by consistently beating opponents you're pitted against.

Matchmaking ratings are bracket specific, hence your 2v2 matchmaking rating will not be affected by how you play in 3v3s, and so on - this rules out some generic ideas of "cheating the system" by bouncing between brackets pulling stunts.

Win rate

A measure certain people use for "success" - how large a proportion of your team's games played you've won. It serves no practical purpose except "epeen flex". Because MMR does not reset between seasons, win rates will tend to be 50-50 on the long run if teams/players don't improve their game play from previous seasons. Often, though, you observe extremely high win rates: 80-2, and so forth. This is typically a result of players setting up a team, intentionally conceding a lot of losses to lower their MMR, and then restarting a new team. This does not, however, grant them higher rating potential or growth, it just means they're pitted against considerably weaker teams early on which helps them gain a higher win rate.


A summary

When you win a game - you gain team rating and personal rating relative to your matchmaking rating. If your team and personal ratings are well below your matchmaking rating, you gain more team and personal rating. The opposite happens if you lose to a team that has a matchmaking rating below yours - you lose. In addition, by winning games your matchmaking rating grows - and goes down by losses. Hence, the easiest way to gain rapid arena rating growth is to beat games consistently.

Team and personal ratings are used to qualify for arena rewards, arena point awarding, and team ranking. Matchmaking rating forms an anchor your team and personal rating slowly slip towards. Eventually, many teams will get stuck on a certain rating range: this is technically the rating range you mostly 50-50 (win rate, yes) your games on, meaning to improve from there, the best answer is to simply become better a player and lose less, win more.

Lovely work! I've added this to the collection of handy PvP guides at the top of the forum. :]