Each Conference is set IN STONE, basically.. year after year and doesn't change unless there's something Big voted on by owners, the Commissioner, etc. (or new teams are added, and that hasn't happened in a while) and the Pats & Colts play in the same Conference (AFC) and played last year, for the Right to go to the Super Bowl and beat the Chicago Bears who were there as the rep. from the other conference (NFC).
There's a long history, for how/why these came about.. and it's all contained in decade of the 1960's.
Most of the "older" teams pre-1960's are in the NFC now (Giants, Eagles, Lions, Bears, old Baltimore Colts, Browns)... and the league that was created as a parallel competitor (called the AFL) was simply merged as the AFC in the late 1960's and was regarded as a weaker conference.. they passed more, the NFC ran more.. better defense, tougher teams played in the NFC than the "new" AFC... (Raiders, Jets, KC Chiefs, Chargers, etc.)... it wasn't until SUPER BOWL III in 1969 that the AFC finally showed it could "play" on the same level, when the AFC's NY Jets shocked the football universe and beat the powerful Colts... (the Jets were a 19 POINT underdog... in the Super Bowl!)... and many say, that game was "fixed" to better merge the leagues, and keep many of the AFC teams from bankruptcy as people were measuring them vs. the older NFC/NFL teams.. every week...
Sooooooooooooooo... what the NFL did.. was shuffle the deck.. and put the OLD NFL/NFC Cleveland Browns that used to play the NY Giants, Packers, Bears, etc. into the new AFC... where they are now... and also, the powerhouse Baltimore Colts with Johnny Unitas etc. were send over to the AFC, as well... after decades of teams moving, franchises ending & being reborn (Baltimore lost the Colts to Indianapolic, but later got the Ravens...) the league has SET the AFC and NFC into stone, like I say...
Even the Dallas Cowboys.. who really are NOT an eastern team by anyone's stretch... are still playing vs. Philly, NY, DC... because what works since the 60's and 70's, still works for the formulas of the NFL.