Definition: The NBA's salary cap is not carved in stone -- teams are allowed to exceed the payroll maximums for a variety of reasons. One of the exceptions to the cap was created to allow teams to re-sign their own players. The Boston Celtics were the first team to employ the exception, exceeding the cap to re-sign Larry Bird. Since then, it has been known as the "Bird Exception."
Players eligible to be signed under the Bird Exception are said to have "Bird Rights." Players must spend three years with a team to earn full Bird Rights, two years for "Early Bird Rights."
For players, having Bird Rights means a lot more flexibility in contract negotiations -- in most cases, players stand to make much more money re-signing with their own teams, rather than leaving in free agency.
Restricted free agents who sign one-year contracts get veto power over trades because being traded would mean the loss of their Bird Rights.
Examples:
Devean George of the Dallas Mavericks vetoed a trade that would have sent him to the Nets because the trade would have meant the loss of his Bird Rights.