Players in the CBA
who qualify for those are known as Qualifying Veteran Free Agents
. Basically, this rule exists to get around salary cap
issues, by allowing a team to break the salary cap
to resign their own free agents, at pay
of up to the player's maximum salary
When a player with this exception is traded, his Bird rights also trade with him. This contract exception can last for up to seven years, and while under this contract, the player can receive up to a 12.5% salary increase, per annum.
The reason that is is known as "The Larry Bird Exception" was that the Boston Celtics were the first team to use it this with...you guessed it...Larry Bird.
There is also a weaker exception known as Early Bird Exception.