New natural rivalries will have the opportunity to grow. This is especially true in the South. Tampa Bay never really fit in the old NFC Central with Detroit, Chicago, Minnesota and Green Bay. The Bucs and Falcons are a rivalry that can turn into a border war. The league has set themselves up for potentially exciting new rivalries.
Players get the chance to play different teams.
In nine years in the NFL, I never played in New England or Oakland. With only three other teams that you have to play twice each year, it leaves the rest of the schedule open to variety that will be exciting for the players and fans. Players get to play in locales they haven't in the past and fans get to see stars their teams haven't competed against. More geographic sense. Arizona moves from the NFC East to the NFC West.