The workplace may not allow you to get to know your boss as a person. Becoming friends with your boss on Facebook may reveal that the two of you share common interests. Shared interests can lead to discussions and opportunities to show your boss you possess qualities that may not come out at work. For example, you might show initiative and leadership skills in your personal life, but your job doesn't give you the chance to exercise those skills. Your supervisor may see that you've got greater potential than your current position allows you to realize. You may want to check and see if your fellow coworkers have also befriended your boss on Facebook before you take the plunge.
Just remember to keep your behavior professional. Some people may feel that the normal boundaries that exist in workplace situations are less strict online. That may lead to unseemly behavior or communication passing between coworkers. You don't want to behave inappropriately toward your boss. And you don't want to encourage your supervisor to behave in an inappropriate way toward you. Unchecked, such activity could ultimately evolve into serious problems, including situations as serious as sexual harassment.