Short answers, pulled from the story.
The American Football League Eastern Division took shape in 1960 with four founding teams. The Buffalo Bills, Boston Patriots, New York Titans, and Houston Oilers formed the initial lineup for this new professional league.
Current members hold nine total titles with six belonging to the Patriots, two to the Dolphins, and one to the Jets. Former franchises contributed additional championships through the Houston Oilers and Baltimore Colts eras.
The Buffalo Bills play in Orchard Park, New York instead of downtown Buffalo. The New York Jets operate out of East Rutherford, New Jersey while sharing a stadium with the Giants. The Miami Dolphins play in Miami Gardens, Florida which separated from the main city in 2003. The Patriots play in Foxborough, Massachusetts rather than Boston itself.
Every team in the division has been led by coaches connected to Bill Parcells at some point. Bill Belichick coached the Patriots while Tony Sparano led the Dolphins and Eric Mangini served as an assistant under both Belichick and Parcells before coaching the Jets.