Company killing is when a player attacks another from the same confederation without warning, similar to the concept in DarkOrbit. Attacking members of the same confederation is not against the rules but is generally frowned upon by some players, especially the newer players as they sometimes get destroyed by more powerful players from the same confederation. As a general rule, you are supposed stick up to allies and lend a hand if they are being hunted. Unlike DarkOrbit however, there are no known penalties to company killing and no protection from them except for the protective seal.
Company killers typically use fast ships with lots of weapons, like the X-class (level 35 trio) combat subs or the elite combat subs. They normally prey on merchant subs as they are slow and not well armed, though the X-class cargo sub still packs a punch and is pretty fast.