Buffy is a normal girl with some not so normal responsibilities. Buffy recently moved to Sunnydale after being expelled from her school in L.A -- something about burning down the Gym. Her parents are divorced, and she lives with her mom.
Buffy wants to be normal, and to have a normal social life, but she can't. Buffy is The Slayer -- The Chosen One -- the only person that stands between Sunnydale ... and a clan of blood sucking Vampires. Instead of carrying her school books around in her knapsack, she carries a collection of crosses, wooden stakes, and holy water.
Buffy depends on her friends (especially Xander and Willow) more than she admits. They are they only ones who really understand the responsibility she faces. She could never tell her Mother what she does at night, and Giles is, well, her Watcher. He sympathizes with her wanting a social life, and is her voice of reason, but Xander and Willow are the ones who understand.
When Buffy meets Angel, she first develops a crush, then falls for him -- only to find out he's a Vampire with a soul. She loves him, but knows they ultimately have no future together.