What defines one "season" of anime?
The 13 week "season" that refers to a time of year or when a show starts airing is sometimes referred to as an "airing" season or a "television" season. This is like "Winter 2013 season". But since shows sometime span different television seasons, even if it's 13 episodes long, this run of a series can also be referred to as a "season". 

Sometimes shows get cut off, go on hiatus, or for whatever reasons (e.g. financial) have a significant break between certain episodes such that the TV series runs through multiple "television seasons" (e.g. Girls Und Panzer) yet the show itself is still referred to as the "first season", and this is sometimes referred to as a "cour" or "series". The usage of "season" comes down to semantics. Multiple "seasons" of a TV series can also be called "series", like Galaxy Angel and it's multiple (different lengths) "seasons" are sometimes called "series 1", "series 2", etc. "Cours" however, usually refer to a 12 or 13 stretch of episodes. So a 26 episode series can be referred to as "2 cours".

But as far as the length of an anime "season", a 12 episode series run can be referred to as a "season", yet sometimes a 26, or 36, or 201 (Gintama) episode run is called a "season". It's technically not tied to a specific length, which is why some people prefer to use "cours".