Game Rating - Used to determine who did better or worse than you in a single game
TrueSkill - Used to adjust your skill after a single game by factoring in who did better or worse than you and whether or not that outcome was expected
Division - A way to group players together based on their TrueSkill relative to everyone else's TrueSkill in the playlist
Daily Rating - Means absolutely nothing, other than ensuring you've played enough games to be put into a Division
Average Rating - Means absolutely nothing. There is a huge difference between averaging 1500 in Steel and averaging 1500 in Onyx
If you want to get a good rank in Arena, your goal is to get the highest Game Rating compared to everyone else in every game you play. To get a high Game Rating, you want to maximize your kills and assists, while minimizing your deaths and betrayals.
Short Version- Do better than the other players in the game every game.