This is a format of overtime in which the first team to score points, whether by touchdown, field goal, or safety, wins the game.
Prior to 2010, the NFL allowed ties during the Regular Season. Donovan McNabb, former quarterback for the Eagles, was famously confused after a 13-13 tie game on November 16th, 2008 versus the Cincinnati Bengals because he did not know ties were allowed in the NFL. Many casual fans were also shocked that ties could occur. The League took notice and put the current "modified" sudden death rules into place for the playoffs in 2010, and began applying them to the regular season in 2012. Prior to 2010, and since 1974, sudden death was exactly as it sounds. The first team to score in overtime wins. The modification now in effect gives each team a chance to score, unless the receiving team scores a touchdown on its first overtime possession. If the receiving team only scores a field goal, the other team is given the opportunity to possess the ball.