This is a phrase used in sports, such as football, to describe the series of games which take place after the conclusion of the regular season. This phrase is sometimes used interchangeably with "playoffs." This is because the post-season is typically made up of a series of playoff games. If a league does not use a playoff system and instead goes straight to the championship game, that game would take place in the "post-season." However, most every modern, professional league in every major sport uses a playoff system to determine who plays in the championship game.
In the NFL, the post-season consists of three rounds of playoff games which culminate in a final championship game. The championship game in the NFL is known as the Super Bowl and has been played every year since 1966. It is played by the winners of the two conferences which make up the NFL, the NFC and the AFC.