A gigabyte is a unit used to measure computer storage capacity and is approximate to 1.07 billion bytes (1024 bytes to the third power).
A few common abbreviations are GB or Gbyte (note that they must be capital).
A gigabyte is normally used to measure the amount of capacity in RAM and HDDs.
Recently, the exact capacities of a GB have come under fire and Creative was sued over the stated amount of capacity in their media players.
More info here:
Creative settles MP3 player capacity lawsuit (2 May 2008)