This isn't a rumor or breaking news or even a link to a newspaper source. That's because there's been no definitive new news regarding Pierce's contract status and I haven't been able to find an article that has explained it in great detail yet. However, here's my quick take.
Paul Pierce is going to remain a Celtic. If he picks up his option to stay, he'll be paid $21M for next season. If he opts out of his last year to become a free agent, the intent will be to restructure his deal to add years to it. The big value there is the uncertainty of the year after next where the league faces a collective bargaining agreement battle. If there's a prolonged strike or lockout, it could prevent free agents (like Pierce would be if he doesn't restructure his deal) from getting another deal. If the work stoppage lasts all year, all the players could lose a whole year of money and a free agent like Pierce would be that much older.
Lots of stuff can happen in a year, especially at Paul's age. So his best interest might be to lock in now to a 3 year deal (or more if he can get it) and ensure that he retires on his own terms as a member of the Boston Celtics.
The value to the team would be to free up cash this year to make some additional moves - perhaps mostly to resign our own free agents. However, because of the other contracts on the books, in particular Kevin Garnett's, there isn't any room to bring in a max or top tier free agent.
So the opt out option would appear to be a way for both the Celtics and Paul Pierce to enhance their positions a bit and help each other meet their goals.
Note: I'll leave the complicated math and finer points to the experts. Please feel free to add more in the comments or provide me with links to any sources that explained it better than me.