It depends on a lot on the type of serial killer.

Mission based killers, basically their convinced that taking these lives is adding up to something tangible. To them each kill is the satisfaction you get from success of completing a really hard task that will benefit your life down the line.

Power and Control killers, its not so much taking the life, more that each time they do so they prove to the world their better than the person they just killed. To take a life is the ultimate form of control over another human being.

Visionary killers are usually insane, they honestly believe that either something is commanding them to kill or that the person their after must die for some reason.

Finally hedonistic killers, simply take pleasure out of the act itself. Their most often sexual homicides, but it doesn't need to be. Their generally split into three subcategories: Lust Killers, Thrill Killers and Comfort Killers.

There are other sub categories, but generally those are the four main motivations (their are also cases where the person is simply so far gone they honestly can't stop themselves from killing, but their extremely rare).

However, most of the time it can be boiled down to the idea that they have a hole in themselves. One that they need to fill, and that is usually done by killing.

The twisted thing about serial killers is often the actual killings the point their least interested in. Usually their thrill comes from all the preparation and ritualistic elements that build up to kill.