Civilians are pretty much any NPC except Confed police officers walking around on any planet or base except one of the Pirate bases. Stealing from, or even killing, a civilian incurs a fine, to be payed on Port Newton (Loye system), and, in the case of murder, also a temporary ban from the planet where you committed the crime.
Attacking a civilian will not only turn any police officers hostile who witness it, but also some of the other people nearby. This means if you start a brawl in a crowded place, like a bar, you might quickly be confronted with a mob of angry civilians making escape difficult.
Advanced Fixer missions often call for assassinating an individual civilian, who are usually accompanied by one or two bodyguards. There are two basic strategies to do this: quiet or quick. Quiet means you wait until the target is in a room or corner where you cannot be seen and then kill them and any and all witnesses before they can call for help, e.g. with a grenade. Quick means you stay as close to your ship as possible, kill the target from afar e.g. with an MPR-481 Pulse Rifle, then flee before anyone can retaliate. Smoke grenades might aid either strategy, however consider that the time throwing them might be better spent running away.
Note that the planet- or base-wide ban for murder is already in effect before you lift off. Specifically this means as soon as you are seen killing someone you are not able to use the planet's Autodoc any more.