The Slayer line was originally created by a group called the Shadow Men who wanted a champion to fight the forces of darkness. They infused a girl with the power from the heart of a pure demon.
The slayer possesses strength, speed, agility, stamina, senses, and endurance that are well above that of a normal human. There is also a mystical side to the slayer, an ability to communicate with slayers of the past and see the future in her dreams.
The name for an apprentice, or uncalled, slayer is "potential."
A new slayer was traditionally "called" during her teens after the death of her predecessor. Willow Rosenberg has since changed the rules and called thousands of girls. It’s unclear how the slayer line continues now.
Examples of Slayers from known Buffy the Vampire Slayer canon yet haven't appeared in comic book issues as of yet:
Amanda - She was a potential who went to school with Dawn. She didn't survive the final battle in the Hellmouth.
Caridad - Was another potential who arrived in Sunnydale. She survived the final battle in the Hellmouth.
Chao Ahn - Another potential that arrived in Sunnydale. She survived the final battle in the Hellmouth.
Dana - Was recently called slayer. Dana had been residing in an asylum after the abuse she suffered as a child. She broke out after she was called. After an incident with Spike and Angel, Andrew Wells along with a team of Slayers took her into custody presumably to help her.
Kendra - She was the slayer activated after Buffy was killed by the master. She was trained from a young age by her watcher Sam Zabuto. Kendra later met Buffy when she journeyed to Sunnydale and became her ally. Kendra was killed by the vampire Drusilla while trying to protect Willow.
Shannon - A potential slayer that managed to get to Sunnydale. On arrival she was nearly killed by Caleb. She survived this and also the final battle on the Hellmouth.