In the US, the state laws governing when deadly force is justified in self defense can be broadly divided into three categories: (Note--I am not a lawyer, and although I am attempting to be accurate, I'm nearly certain to get some details at least slightly wrong)
Stand Your Ground--In a place you have the legal right to be, you are not required to retreat from an aggressor, and if attacked may use deadly force if a 'reasonable person' under similar circumstances would believe that the attack was likely to cause death or grievous injury. Without Stand Your Ground, self defense is generally regarded as an affirmative defense--In order to use the claim in a criminal trial, the victim of an attack who claims self defense has to essentially plead "Guilty but justified", then prove justification. Stand Your Ground means that someone claiming self defense remains "presumed innocent" until there is enough contrary evidence. As long as they are presumed innocent, they aren't arrested without that contrary evidence. Most stand your ground laws also include some form of civil immunity--If you are defending against a person committing a felony, you cannot be held civilly liable for injuring or killing them unless you are found guilty in the criminal phase. This is based on civil rules rather than criminal, so a preponderance of the evidence rather than beyond reasonable doubt.
Castle Doctrine is similar to Stand Your Ground, but in limited locations--It applies at home. Depending on the state it may apply when a guest in someone else's home, in your car, or in the workplace.
Duty to Retreat is the situation where neither of the above concepts are a defense--Where a victim is required to retreat before using force. In the US, there are only a few states that have a duty to retreat, and even in those states case law generally gives at least some of the features of Stand Your Ground, sometimes via case law rather than through legislation.
Stand your ground is irrelevant in determining the verdict in the Zimmerman-Martin case. Its application in criminal trials is in an extremely narrow set of circumstances--where a victim is in a place he has the right to be, realizes that an unwarranted violent attack is imminent and recognizes a viable escape route available that does not increase danger to the victim or people he is responsible for.
In no scenario from either side is there an opportunity for escape. If Zimmerman was the first to initiate violence, he gave up his right to self defense with or without SYG--in that case, the jury came to the wrong verdict. If Martin jumped Zimmerman, then there was no opportunity for escape, again SYG does not apply. Being followed is not by itself justification for violence. It is unlikely that Zimmerman could run backwards faster than Martin could run forward.
I've seen quite a few comments that Zimmerman-Martin shows that SYG is wrong and needs to change--but none of them explain how it would have changed the verdict here, or how it would help in general. Instead I've heard "A Zimmerman juror mentioned it", or "someone might think they can shoot someone and get out of it just by claiming to be scared". In some cases the people making these claims are lawyers and politicians who almost certainly know better--but believe that their audience does not, and that confusion on the issue will increase support for gun control.
Personally, if I've ever got the choice between running to safety and shooting or killing someone, I'll run even if the law doesn't require me to. I still support Stand Your Ground--in large part for its civil immunity. Someone committing a felony should not be able to sue their victims unless the victims commit a crime against the felon at least as serious. There is also the timing problem--the prosecution has weeks or months to find the escape route you missed in the few seconds you had available. As a general rule, I think people who initiate violence should have far less rights than those who are defending.
Opponents call Stand Your Ground a "Shoot first" or "Make My Day" law, claiming that it allows people to shoot any time they feel vaguely threatened, and that it will result in blood in the streets. The law almost always has a "reasonable person" clause, in that the threat has to be considered valid by a reasonable person under the same circumstances with the same information. We also have decades of experience in most states,
"He was unarmed" "It was just going to be a beating, not worth killing over". It is entirely possible to kill with bare hands and feet, so self defense (even without SYG) allows self defense--often requiring a disparity of force. The disparity may be 2 against one, young vs old, man vs woman--or may just be an avid and able fighter vs someone who hasn't been in a fight since grade school. (In the last case, it might be that the disparity isn't evident until the victim begins to lose the fight).
"Stand Your Ground is inherently racist". Recent studies have shown that the Florida law is claimed disproportionately by minorities, and that they are disproportionately successful. We have recently had at least one case quite similar to the Zimmerman/Martin incident, except the shooter was black, and his attackers were both white. Very little news coverage.
"It means you can't arrest anyone who claims self defense". No, it means you need a preponderance of the evidence that it was NOT self-defense in order to arrest--that would be 50.1% that the accused is guilty. Meanwhile, the standard for a conviction is "beyond a reasonable doubt"--this would have to be at least 95% positive (I'm more inclined to go with Ben Franklin's "better 100 guilty escape than one..."). If you cannot prove above 50%, what are the chances you will be able to prove 95 or 99%? Should you really arrest someone you probably can't convict?