The gun means the user walks away from conflicts to avoid using it for anything other than stopping an aggressive and harmful attack, on self or others, that cannot be resolved in some better manner.
It is a good sentiment, and I agree with it. But my understanding of Stand Your Ground is this is not the case where SYG is the law. Thus, the name of the law. It is possible I do not understand.
Self-defense laws vary by jurisdiction, but in the United States, for the most part, a number of conditions must be present for a legitimate claim of self-defense:
1) The individual must believe he is in imminent danger of death or serious injury;
2) That belief must be held for valid reasons;
3) The amount of force used to prevent the threat of death or injury must not be greater than reasonably necessary to prevent the threat; and
4) Before using force for self-defense, the individual must first make an attempt to flee from the aggressor if such an attempt is feasible.
There are some other details as well -- for example, if you see a woman getting raped, you're allowed to use force to rescue her; if you're trespassing and the landowner confronts you, you have no claim of self-defense, that kind of thing. But the above list is the big stuff.
All that "Stand Your Ground" laws do is remove condition number four -- the other three elements remain in place. To give a more concrete example: You're walking down the street somewhere, minding your own business, perhaps carrying a gun/baton/pepper spray/whatever, or maybe you're just a skilled martial artist. You get the idea. A thug comes up to you and pulls a weapon.
In a state without a Stand Your Ground law, you may not use your gun, baton, or martial arts skills to protect yourself, at least, not yet. First, you have to try to run away from the guy if there's a reasonable chance of being able to escape, and if you proceed to use of force before attempting to flee, you can be charged with a crime -- typically some form of assault and/or battery, or even homicide if you end up killing the guy. You may only use force to protect yourself if escape is not feasible, or if you've attempted to escape and failed to do so.
In a state with a Stand Your Ground law, however, you may proceed directly to use of force in self-defense. (You can still try to run if you want, but you're not legally obliged to.) It is called a "Stand Your Ground" law simply because it removes the duty to retreat.