bird rights. i'm actually just reading up on it right now lol
so apparently bird rights is players who have played 3 years with a team. these can also be transferred via trade. for example if a player gets traded during his 3rd season, the team acquires his bird rights as well. the warriors can resign bird rights players up to max.
then there is the no-bird exception, which is what durant is doing, after being there only 1 year. this guy explains it well. basically can resign but only up to 105% of current salary. theres also the early bird exception which is 2 years instead of waiting 3 years. "While Bird players can receive maximum salary deals for up to five years, the Early Bird exception cannot be used to offer a max deal. The most a team can offer an Early Bird free agent is 175% of his previous salary or 104.5% of the league-average salary, whichever is greater. These offers are also capped at four years rather than five, and must be for at least two years."
there are also more exceptions im too lazy to read about, but here's the link if you're interested: http://www.cbafaq.com/salarycap.htm#Q25