Two conferences, four divisions in each. Each division winner, plus two other "wild card" teams in each conference make the playoffs (so six in each conference).
To illustrate, Philadelphia and New York are in the same division (The NFC East) and they're both 9-4 right now. One will be the division winner. The other has a shot at the Wild Card, but they have to be worried about every other team in the same conference (New Orleans is 10-3 and Green Bay is 8-5). So two of those three will make it, but it's hard to say who just yet.
EDIT: Tampa Bay is also 8-5. So there are four teams who are hoping for that Wild Card spot (Tampa Bay, New Orleans, and Atlanta are in the same division and will be fighting for the division championship too).