A Slayer, in the fictional Buffyverse established by Buffy and Angel, is a young female bestowed with mystical powers that originate from the essence of a pure-demon, which gives her superhuman senses, strength, speed, endurance, agility, and healing in the fight against forces of darkness. She also receives prophetic dreams in the few hours that she sleeps.
The Prophecy of the slayer states, "Into each generation a girl is born: one girl in all the world, a chosen one. She alone will wield the strength and skill to fight the vampires, demons, and the forces of darkness; to stop the spread of their evil and the swell of their numbers. She is the Slayer."
While they are commonly referred to as "Vampire Slayers", even by Watchers and vampires themselves, their "jurisdiction" does not just include vampires.
In ancient Africa, a group of tribal elders known as the Shadow Men use powerful magic to infuse a captive girl with the heart, soul and spirit of a demon. This process grants the girl great strength, agility, and endurance: she becomes the First Slayer, called to fight the vampires and other demons that populate the earth. The Shadow Men's descendants go on to form the Watchers' Council, an organization dedicated to finding, training, and supporting Slayers.
Due to the violent nature of the life of a Slayer, their average lifespan is quite short after being called. Consequently, the Shadow Men's spell also created a large number of Potential Slayers - normal girls around the world who may one day be called. When a Slayer dies, one of the Potentials - seemingly chosen at random - gains the powers and abilities of a Slayer. The Watcher's Council tries to identify and train these "Potentials" before they are called, locating some as babies, but are not always able to do so, with some girls only being found after they have been activated as the Slayer.
This process continues through the generations until 1997, when one Slayer - Buffy Summers - is killed in battle, only to be revived via CPR. Buffy retains her Slayer powers, but her clinical death is enough for the next Slayer to be called. For the next several years, there are two Slayers in the world: first Kendra, who was called on Buffy's death, and then Faith, who was called when Kendra died, approximately one year later.
Whether or not Buffy's second death called another Slayer is not known, but what is clear is that her second resurrection for some reason caused an imbalance in the Slayer line. Following her first death, Mayor Wilkins says that he doesn't want Buffy killed, because that will cause a new Slayer to be called. Following her second death, Buffy herself, addressing a group of Potential Slayers, says: "My death could make you the next Slayer." However, the shooting script for the final episode on the show originally included a much longer speech by Buffy to the potential Slayers, including the line "It's true none of you has the power Faith and I have. I think both of us would have to die for a new Slayer to be called, and we can't even be sure that girl is in this room. That's the rule. So here's the part where you make a choice."
The mystical "rules" governing the Calling of Slayers change again in 2003, when Buffy discovers a Scythe forged for the Slayer to wield. Willow Rosenberg uses magic to tap into the Scythe's essence at Buffy's request, and performs a spell that calls every living Potential Slayer at once, thus ending the legacy of "one girl in all the world".
After taking the time to find and count them, Buffy states that there are at least 1800 Slayers in the world. Exactly how the Slayer line continues after this is currently unclear, though from Buffy's speech ("From now on, every girl in the world who might be a Slayer will be a Slayer"), it's possible to presume that every future girl who would normally be born a Potential Slayer will instead be born an actual Slayer.
At some point in the 21st century, a Slayer faces an army of demons. As a result of this battle, all demons and magicks are banished from Earth's dimension. At this point, the Slayer line becomes dormant - while Potential Slayers still exist, none are called for two hundred years.
In the far future, demons eventually find a way to return to Earth's dimension, and the next Slayer is finally called - a girl named Melaka Fray. The continuity of the Slayer line is still unclear since Melaka had a twin brother who was given the dreams and visions typically possessed by the Slayer, while Melaka received the physical attributes (strength, reflexes, stamina, accelerated healing). On top of that, Melaka's brother has died and become a vampire.
Faith Lehane is able to pick up the vampire Angel with one hand and easily throw him short distances, lift him over her head, and slam him into the ceiling. Once, while fighting Buffy, she punched her fist into a wall. She is also seen picking up a bar bell with one hand and hitting a woman in the face with it (the woman was trying to kill Faith at the time).
Melaka Fray is able to pick up an overweight vampire several times her own size and body mass, lift him up over her head with both hands and throw him over a distance of presumably over 20-25 feet, with no downward arc to his trajectory (which was only interrupted due to his hitting a metal grate, which was extensively deformed on impact).
The psychotic Slayer Dana is able to, through several violent shoves, knock down a metal door as well as deform the edges of a metal gate as she tore it from its hinges.
However, the Slayer is far from invulnerable. For instance, Buffy has been knocked out by blunt force trauma, such as being hit over the head with a lead pipe by a possessed Cordelia Chase in "Bad Eggs" and with a detached mannequin arm by Ethan Rayne in "The Dark Age". In addition, the Slayer can be injured by conventional bullets, bladed weapons, and more advanced weaponry (such as the energy weapons commonly used by the Initiative) just as easily as an ordinary human can, but they can recover from even very severe injuries in remarkably short periods of time. Usually, Buffy is completely healed within 24 hours of being injured, though more serious injuries have been shown to take at least a few days. Buffy has survived contact with a live electrical wire; the normally lethal jolt simply renders her unconscious.
A Slayer also has the limited ability to detect the presence of vampires (and presumably other demons). This power must be honed as with the heightened awareness, and the Slayer must focus to achieve the full effect. This does not prevent Buffy (and other Slayers) from being ambushed by vampires. Buffy is unusually deficient in this sense: Although she initially distrusts Angel when first meeting him and seems to sense that he is following her for a period of time she doesn't realize until he shows her his vampiric face for the first time that he is a vampire. Kendra also displays this ability in inconsistent terms; she knows Angel is a vampire after seeing his vampiric face at the skating rink but she does not know that Buffy isn't, she merely assumes she is because Buffy and Angel were kissing.
In the film, the ability to detect vampires manifested itself in the form of feminine cramps. (Merrick describes this as an "natural reaction to their unnatural presence.") This ability was inconsistent, as Buffy was unaware that a vampire was hiding in a photo booth right next to her. The movie, however, is not considered canon, and this aspect of her powers was not carried over to the series.
Melaka Fray, the Slayer of the far future, lacks these abilities. Due to the unusual nature of their birth, her twin brother received these visions instead.
Overall, the Slayer's abilities seem to be enhancements of normal human attributes, rather than extra abilities garnered from a magical source; Buffy trains constantly and works out to enhance and maintain her abilities, suggesting that they would atrophy otherwise. A "normal" workout routine that would enhance a regular human's strength and speed increases her abilities much faster and at greater magnitude . Also, the concoction created in the Season Three episode "Helpless" (which Giles says includes muscle relaxants and adrenal inhibitors) would have the same effects on a human as they did on Buffy; the effects are simply more pronounced. Also, regular illnesses such as the flu were shown to have effects on the Slayer not greatly different from its effects on humans; once again the handicap is more noticeable given the Slayer's usually enhanced abilities. .