Back-story

A character's back-story is the tale of who they are, where they came from, what formed their aims and ambitions. The back-story is often used as a device to explain the players more unusual character creation choices (Unlikely? A drow ninja-barbarian? Look, I have a good explanation...) and of course as a hint list to a DM of the player's wants and needs.
A good back story includes:

• Family - all DMs like to know about potential allies and rivals, hostages and patrons.
  
• Youth - knowing where a character came from is a great aid in making adventures seem relevant to the character.
  
• Hooks - it's good to know that a character seeks the lost knowledge of Atar the Lost, seeks revenge for the murder of their father, hates goblins with a passion, was saved from death by an elf and owes a life-debt to the sidhelien and the like.
  
• Story - you can just list the points you want to cover, but it's more fun as a DM to read a small story-style list.
  
• Fluff - some players build not just who their character is, but details of their home village, people they know, etc, etc. These creations are unlikely to be unchanged by the DM in use, but can act as a good springboard and shortcut for the DM.