There is a right under the United States Constitution to a speedy trial in criminal cases, and that right applies via 14th Amendment to the United States Constitution to state governments.
The federal government, and every U.S. state operationalized that constitutional right through a statute setting strict deadlines by which to conduct a trial in criminal cases, which so long as it is compliant with case law regarding the longest delays that are constitutionally permissible, will control.
This right can be, and routinely is, waived by mutual agreement of the attorneys for the prosecution and the defense.
The defense does this both because (1) if their client is out on bail, this secured certain freedom until the trial, and (2) defense attorneys hope that an otherwise solid case that would result in a conviction if brought to trial quickly, might deteriorate with delays, for example, due to witnesses becoming unavailable or forgetting what they saw, and evidence being misplaced.
Usually, the defense does this when the defense believes that a conviction is likely if the defendant take the case to trial, but the client is not willing to accept the best plea bargain offered by the prosecution (which in a strong case for the prosecution may be simply the right to make an unconditional plea of guilty to all charges filed).
Prosecutors do this because (1) if the defendant is incarcerated, they will have caused the defendant to serve time without regarding to a trial outcome and this may cause a fairly just time served sentence in the eyes of the prosecutor which can be used in a plea bargain, and (2) prosecutors are very busy and need more time to prepare their cases for trial. Prosecutors also worry that failure to allow the defendant sufficient time to prepare when the defendant requests it, could be a basis for an appeal overturning the conviction in a high profile, high stakes case. Prosecutors most often favor extensions of time when the defendant is incarcerated pending trial and when their case is weak.
The last time I looked there was some division of authority over the question of whether a prosecutor had a right to insist on a speedy trial, or if this right belonged only to defendants. My recollection is that the majority rule was that the prosecution could also insist on a speedy trial.
Of course, it is entirely possible for the defense to think it has a weak case and for the prosecution to also think that it has a weak case, even though those things generally aren't simultaneously true. This is mostly because evaluating the strength of a case is a subjective matter that requires weighing myriad factors that go into the strength of a case.
Extensions of the speedy trial deadlines secured with the consent of defense counsel do not count against the time limits, nor do delays caused by certain tactics of the defense. But, the defense can stop granting extensions of time and force a trial at any time.
Usually, it is considered an appealable abuse of discretion for a judge to insist that a case go to trial in the face of a stipulation of both the prosecution and defense counsel to continue a trial and waive the right to a speedy trial, so long as some plausible reason is provided to the court to justify the delay.
But, there was one notable case where the defense counsel (for some very good reasons) was agreeing to extensions of the speedy trial deadline over the express direction of his client who stated repeatedly in open court in a federal criminal prosecution in the Second Circuit that he wanted to exercise his right to a speedy trial and have a trial as soon as possible. In that case, after many years, the judge was ultimately required to dismiss the case because the right to a speedy trial was denied, because the client and not the defense attorney is ultimately the person who has the right to decide whether or not to invoke the right to a speedy trial and the client has a unilateral right to refuse to grant further extensions of the speedy trial deadlines.
In the case you mention, the defense waived the right to a speedy trial in writing on July 7, 2014 after previously having done so orally in March of 2014. The defense counsel is likely doing everything it can to delay the trial so that their client can remain free on bail for what may be a substantial share of the rest of their client's life.
Approximately three years of the pre-trial proceedings involved pre-trial "discovery" which involved document disclosure by the prosecution and pre-trial depositions of the numerous witnesses identified by the prosecution in the case. Another year or so was devoted to motions practice over excluding evidence and related to procedural provisions for claiming self-defense prior to trial under Florida law. Once those matters we wrapped up and the case was actually ready to be tried, the judge set the case for the first available slot on the court calendar with enough time to select a jury and hear the lengthy presentation of evidence at trial.
Higher Level Analysis
The answer above is the canonical one and mechanically explains the result.
At a deeper level, scholarship about American civil and criminal procedure also blames the extreme finality of U.S. jury trials for the delays.
In most Continental European systems, if you don't like the result of your first trial, you can have a second trial in a higher court at which not just the law, but the evidence may be reconsidered. So, a surprise in the first trial isn't a catastrophe.
In contrast, in a U.S. jury trial, factual findings of a jury can't be reconsidered on appeal, only legal decisions of the judge, and an acquittal can't be appealed at all. So, a huge amount of time has to be invested by both sides in preparing for highly unlikely possibilities at trial because once it starts you only have one shot and there is little or no time to react to surprises. In the end, as a result, it often takes longer to conduct one trial in the U.S. than it would to conduct an initial trial and a trial de novo in a higher court on appeal in European criminal cases.