The right to a speedy trial is guaranteed by the Sixth Amendment of the U.S. Constitution. It ensures that defendants will be brought to trial for their alleged crimes within a reasonable period of time after arrest. It also gives them the right to a jury trial, depending on the crime.
Under Florida's law, defendants charged with a felony -- like George Zimmerman, who's charged with second-degree murder in Trayvon Martin's killing -- must have their case heard within 175 days. For misdemeanor defendants, it's 90 days.
In general, if a case isn't brought to trial within the time limit, defendants can seek to have their charges dismissed because of undue delay. While that might sound good for the defendant, it doesn't happen too often.
So back to the original question. The reason why most attorneys waive their client's right to a speedy trial is so that they can ask for more time to prepare a defense. That's exactly what O'Mara did, and in general, that's why it's usually done.