Battle Rating BR is used to balance out planes based on how well they fight, or how dangerous they are. In realistic battles , you have only one plane and it's BR is used to match you with approximately equal enemies. Usually you should not be put up against planes that are more than 1BR higher or lower than you. In arcade mode it's a bit more complex.
Battle Rating Calculation
Battle Rating Calculation | War Thunder Wiki | FANDOM powered by Wikia
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Battle ratings are used by War Thunder to determine matchmaking in-game. Battle ratings are calculated by examining how well an aircraft or ground unit fares in different game modes, and they may differ for each game mode for the same vehicle for example, an aircraft or ground unit may perform considerably better in arcade mode than realistic battles mode, and so will have a higher battle rating in the former. This allows for a balanced game at all ranks and using all vehicles, meaning that certain nations having technological advantages at different periods in the game's timeline is not an issue when playing, and planes that are too powerful do not ruin gameplay for those flying less effective aircraft.
Matchmaking is better known to players as the "balancer," but this mechanic in War Thunder is called matchmaking for good reason. Unlike simple team selection systems, designed only to balance out the game sessions, the capabilities of War Thunder's system are much broader. It allows you to create sessions with strictly defined vehicles, restrictions on certain types and classes and various other configurations.