I've learned that, in every story, there is a big, bad something. An evil force that, no matter the size, corrupts the world of the story, and tries its best to destroy the hero. A wolf, a witch, a giant, a dragon, a knight... or an idea, a desire, a temptation... or even a book.
A Big Bad could be a character with Evil Plans or it could be a situation, such as a comet heading towards the Earth. It is behind all of the other bad happenings. The Big Bad can (and often does) exert effect across a number of episodes, and even an entire season.
Note that Big Bad is not a catch-all trope for the biggest and ugliest villain of any given story. The Badass leader of the outlaw gang that the heroes face once or twice is not the Big Bad. The railroad tycoon who turns out to be using the gang as muscle is the Big Bad. In general, if there is a constant Man Behind the Man story going on in order to reveal the big bad, then whoever is behind it all is the Big Bad, not every major villain in the lead-up. At other times, if a new enemy shows up to replace the previous Big Bad, then they are the Big Bads of their individual storylines.