A speedy trial demand is exactly what it sounds like: You are demanded to be tried in a timely manner, and if that doesn't happen then your case will be dismissed. Whether to file one is a strategic choice that depends on the specific facts of your case.
The benefit is that your case is fast tracked. The prosecution has less time to investigate, locate witnesses, perform forensic tests, and otherwise prepare the case. But this cuts both ways; your lawyer also has less time to prepare a defense, discovery issues are waived, and you may find yourself at trial and unprepared.
Call me at 404-909-7795 to talk about whether a speedy trial demand is right in your case.