Many serial killers are sadistic sociopaths. They feel no empathy. From an early age they were abusive and violent. As children they would torture and kill small animals. After a while, fantasy and animal abuse aren't enough, and they move on to people.
Many of them are sexually motivated. They are turned on by violence, arson, mutilation, cannibalism, necrophilia, and they want to act out their fantasies.
Some of them have an agenda, they want to take out their frustrations on other people. Many have a particular type of person they kill, someone who resembles someone they knew once, or the kind of people they hate. Some kill because they can't handle interpersonal relationships, and killing someone and having sex with the body is the closest they can get.
Some kill for profit.
Some serial killers start as rapists, their crimes escalating and becoming more violent as time passes as they "go too far."
Some think they're doing the right thing by killing people. Perhaps misguided religious zealots. They might be schizophrenic.
There's question as to whether serial killers are born or made. Some serial killers had terrible childhoods, traumatic experiences when they were children. Would these people have become murderers if they had been raised differently? If their mothers had shown them more affection, would they have had the empathy they now lack? Maybe they have some sort of chemical brain imbalance, or brain damage, or they were just born "wrong." It's really hard to say.
But it's all these unknowns, what makes a person into a serial killer, how can it be prevented, that makes serial killers so interesting.