Complex sentence: Leeman Bennett, the former head coach of the Atlanta Falcons and Tampa Bay Buccaneers, served as chairman of the selection committee, which had the task of picking the best teams from those made available by the selection criteria set by the two conferences.
Split into simpler sentences: Leeman Bennett, the former head coach of the Atlanta Falcons and Tampa Bay Buccaneers, served as chairman of the selection committee. This committee had the task of picking the best teams from those made available by the selection criteria set by the two conferences.