Wikipedia has a pretty good synopsis of the case in my opinion.
short version....
G.Z. claims he was armed because he was afraid of a loose Pit Bull roaming the neighborhood. (he was also NOT on duty that night). He was on his way to the grocery store when he spotted T.M. G.Z. claims he was on his way back to his truck when he was confronted by T.M. and implies that he was immediately assaulted by T.M. Thus, had to use deadly force to protect his own life.
T.M. account of the events are probably very different from G.Z, but he's dead so we don't get to hear them. We only get to piece the events together through a phone call he was on with R.J.
It boils down to who you believe.
People on T.M. side claim that G.Z. initiated contact first. Even if it was only verbal contact, it was still contact. And that escalated to the tragic events that happened that night.
On the G.Z. side, he did nothing wrong at any point and was just honoring his oath as neighborhood watch coordinator. He was assaulted by T.M. as he jumped out of the bushes and G.Z. was left with no other option than to defend himself.
Personally, I believe the truth lies somewhere in the middle. Purely conjecture on my part, but I think G.Z. did verbally contact T.M. and there was a heated conversation. Maybe even some pushing and shoving. G.Z. left and started walking back to his truck, but T.M. was pissed and followed G.Z. The altercation got even more physical and G.Z. was getting his ass kicked. He got scared and shot the kid.