Every team in college basketball plays in a conference - the regular season consists of each team playing other teams in their conference.
Conference size and structure vary (mostly between 8 and 16 teams) - you need to look at an individual conference to see how it works.
All teams generally also play a number of games during their season against non conference opponents.
In NCAA Div I there are 32 conferences - the 64 team "post season" consists of the 32 conference winners, plus one other team from each conference invited by a committee to play post season. This may be the conference runner up, but may also be a lower team if they have performed well over the season (there is a complex ranking system that helps sort this out).
Hence the Div I post season is 64 teams who are all seeded, play through knockout rounds down to the "sweet sixteen", the "elite eight", then "final four" and finally the championship game.
Div II only has 23 conferences, so post season is not as large but a similar system.
Check out this link for conference information and team maps.
http://en.wikipedia.org/wiki/College_basketball