1. Yes, the law does mean you can use deadly force against an unarmed person (sometimes).
The law says, "A person is presumed to have held a reasonable fear of imminent peril of death or great bodily harm to himself or herself or another when using defensive force that is intended or likely to cause death or great bodily harm to another if:
(a) The person against whom the defensive force was used was in the process of unlawfully and forcefully entering, or had unlawfully and forcibly entered, a dwelling, residence, or occupied vehicle, or if that person had removed or was attempting to remove another against that person’s will from the dwelling, residence, or occupied vehicle; and
(b) The person who uses defensive force knew or had reason to believe that an unlawful and forcible entry or unlawful and forcible act was occurring or had occurred."
In other words, if someone is breaking into your house (or car), you are allowed to (1) assume he is planning to kill you, and so, (2) kill him first. Without this law, you aren't allowed to use more force to defend yourself than the person attacking you (or who you think is attacking you) is using. That is, if they have no weapon, you can't use a weapon either. This law changes that by letting you assume they're using deadly force. The idea is that you don't have to wait and see how much force the person is planning to use - you can shoot first and ask questions...never. It's called "stand your ground" because you don't have to run away.
2. This law can be used to protect domestic violence victims who kill their attackers at home...maybe.
This presumption in the shooter's favor doesn't apply if you kill the house's owner, unless there is an "injunction for protection from domestic violence or a written pretrial supervision order of no contact against that person" (and there are other exceptions that aren't relevant here).
What that means is, you can shoot your attacker even if he lives there too...but only if you already have a restraining order against him.
3. You have a right to "stand your ground" in public places, but in that case, it's not as easy to claim you killed someone in self defense.
The law adds, "A person who is not engaged in an unlawful activity and who is attacked in any other place where he or she has a right to be has no duty to retreat and has the right to stand his or her ground and meet force with force, including deadly force if he or she reasonably believes it is necessary to do so to prevent death or great bodily harm to himself or herself or another or to prevent the commission of a forcible felony."
This means, if someone attacks you in public, you can "stand your ground" - you don't have to run away. But, unlike the rule if someone attacks you at home, you can't assume they're planning to kill you. You can only use deadly force if you "reasonably believe" you need to, to save your own life or someone else's (or to stop a violent felony, like an armed robbery). This is much more like a regular self-defense law: if you kill someone, you have to prove you had a good reason to do it - you don't get the benefit of the doubt. This "public place" law is, of course, the one that would apply in the Treyvon Martin case, not the part that assumes it was ok for you to kill someone.
According to the Slate article linked above, this law is applied with a hearing before trial in which the defendant (here, Mr. Zimmerman) has the burden to prove that he killed in self-defense. It seems to me that, because he wasn't at home at the time, he will have a much harder time doing that. If, that is, someone decides it's a good idea to even try.