A Big Bad is a term applied (mostly by fans and the show's creators, but also spoken in the Buffyverse) to describe major villains on Buffy the Vampire Slayer. Specifically, it is usually accepted to refer to the single villain that, in each season of Buffy, is the dominant and final one.
The Big Bad is typically not only dangerous (most of the Big Bads threaten some version of apocalypse) but also helps articulate the major themes of the season. Some of the Big Bads are built up and present from the season's beginning (or earlier) - i.e., The Master - and others are sprung as a surprise near the end of the season - i.e., Angel.
Little Bad/Big Bad
For some of the show, the seasons followed a pattern in which lesser villains (presumed to be the Big Bad) are introduced, only to later lead to the more powerful surprise Big Bad:
Near the beginning of the season, a villain was introduced who appeared to be a Big Bad and absorbs much of the heroes' attention. Then, suddenly, this 'Little Bad' is rid of (typically killed) and replaced by the Big Bad, usually about halfway through the season.
This pattern in action:
Season 1: The Master
Season 2: Spike->Drusilla->Angelus
Season 3: Mr. Trick->Faith/The Mayor
Season 4: The Initiative/Maggie Walsh->Adam
Season 5: Harmony/Glory
Season 6: Nerd Trio/Warren Mears->Dark Willow
Season 7: Caleb and The First
As can be seen, this pattern is rarely perfect, and the specific instances are often disputed. Unlike the other 'Little Bads', Spike does not die (although it is well known Joss Whedon intended the character to be offed, until James Marsters' portrayal convinced the show's creators to keep him around); the Mayor's presence is well known before Mr. Trick is killed; and Warren dies much later in the season than the other 'Little Bads'. However, Whedon has stated that the true Big Bad of season six was "life."
Nevertheless, creative arguments can be made for different interpretations of the Little Bad/Big Bad pattern. For example, Faith may be interpreted as the true replacement for Mr. Trick in Season 3.