A two way player is an athlete who plays two different positions not on the same side of the ball. This means that they are a part of the offense and defense or special teams, rather than specializing in one position.
In the earlier days of organized professional football, playing multiple positions was not just impressive but it was expected. The "one-platoon system" that was implemented when teams did not have large rosters and were not allowed to substitute players at will. This system featured the best players on each team contributing on both sides of the ball.
The best two way players in history all played in the early 1900's. Bobby Layne and George Blanda both played quarterback and were responsible for field goal kicking. Hall of Famer Chuck Bednarik led the defense as a linebacker and protected the offense at center. His fellow Canton enshrinee Sammy Baugh shined at three positions, quarterback, defensive back, and punter.
There are many other former all-pros who excelled everywhere on the field. It was more common to work at many different skill-sets rather than differentiating early in a player's youth career. There will never be another Jim Thorpe, who played almost every position by the time his career was over.
Despite being almost obsolete, there are still a few athletes in the NFL who line up on most sides of the ball. Patrick Ricard is a fullback and defensive lineman. J.J. Watt will occasionally play tight end in end zone situations. The most common type of multiple position players in the modern era is receivers and defensive backs who double as return specialists.
It is a regular practice in college football for high level athletes to play multiple positions. Champ Bailey and Charles Woodson are both known for their highlight reel catches, on offense and defense, for Georgia and Michigan respectively. Even recent draftees like Adoree Jackson and Myles Jack were acknowledged for their prolific abilities in various situations.
Once athletes leave college, they tend to put one position behind and focus on specializing in the NFL.