ok, here's an explanation from bioware forum on initiative as i myself don't really know how to explain it.
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Initiative determines how fast you go. Every time a combat starts, all participants in the combat roll their Initiative. The person with the highest initiative gets to act first. The person with the second highest goes next, and so on down the list until you reach the lowest. Then you start the next round, and go in the same order until the combat is over.
If you're an archer, having a higher initiative isn't quite as important (I'd think) since distance between you and your opponent means you have the upper hand anyway. But, if you and another ranged fighter are sniping each other, a higher initiative means you'd shoot first...and in some situations, that could mean you kill him faster than he can kill you.
Now let's say you're a rogue and you see a bunch of orcs over in the corner, and they haven't seen you yet. You click on an orc in the front of the bunch.
You roll your Initiative, the orc rolls his. If you win the Initiative roll and make your attack the following things apply:
1) The orcs do *not* get an Attack of Opportunity for you moving into their Threat Zone.
2) The orc that you attack is flat-footed, and gets no dexterity bonus to AC.
3) You get a sneak attack.
If the orcs win the roll, you do not get a sneak attack and are subject to Attacks of Opportunity.
Keep in mind that if your initial attacks kill your enemy, they do not even get a try at attacking you back.
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hope that helps.