Abraham was born in Timmonsville, South Carolina. In his high school years at Lamar High School in Lamar, South Carolina, he was primarily an athlete in the track program, where he set the current South Carolina record for the 200-meter dash, at 22.6 seconds, and ran the 100 meters in 11.26 seconds. He also competed in the throwing events, recording top-throws of 13.61 meters in the shot put and 43.05 meters in the discus. He played organized football for the first time as a senior in high school.
Drafted in the first round of the 2000 NFL Draft, he made an immediate impact for the New York Jets; in his rookie season, he recorded 12 tackles and 4.5 sacks in only six games before being injured. In 2001, he recorded 58 tackles and 13 sacks, and was named to the AFCPro Bowl. In 2002, he recorded 48 tackles, with 10 sacks, and was again named to the Pro Bowl. In 2003, he only recorded 37 tackles and six sacks, due to being injured mid-season.
In 2008, he had a career high 16.5 sacks through the entire season and ranked 3rd in the league that year. Despite the great numbers he was not elected by voters to play in the 2009 Pro Bowl.
On December 12, 2010, Abraham recorded two sacks against the Carolina Panthers. The two sacks gave him 100.5 for his career, making him only the 25th player in NFL history to eclipse 100. On December 27, on Monday Night Football against the New Orleans Saints, Abraham recorded his first career interception after deflecting and catching a Drew Brees pass attempt.
In December 2010, Abraham was selected to his fourth Pro Bowl.
On June 21, 2012, Abraham signed a 3 year $16.72 million contract to remain in Atlanta.
On March 1, 2013, Abraham was released by the Atlanta Falcons.
Abraham signed with the Arizona Cardinals on July 25, 2013. In his first season in Arizona, he recorded 11.5 sacks, which ranked seventh in the NFL, and 4 forced fumbles. Despite a productive first season with the Cardinals, Abraham left the game on September 10, 2014, after a concussion he suffered during a Monday Night Football game against The San Diego Chargers. After the game, he spoke with Bruce Arians for several hours discussing if he should retire. On September 19, 2014, Abraham's 2014 season prematurely ended as the Cardinals placed him on injured reserve due to his concussion.