A strategy used on offense where a lineman is declared an eligible receiver. The lineman has to report to the official that they are eligible, and this allows them greater latitude in movement and alignment. As an eligible receiver, the tackle can lineup in the tight end position. This can give an offense an extra blocker. The other potential opportunity an eligible receiver has is that they can receive a pass, which is sometimes used as a trick play by the offense.
There are two main reasons a team might use a tackle eligible play. The first is to gain a formation with more strong blockers in it. Since a team can put an extra lineman in a position usually reserved for a tight end or other skill position player, it gives the team a larger number of blockers and allows them more strength in the run game. Teams will typically overload one side of the line and attempt to dominate that side of the defense. The other reason to run a tackle eligible is to allow the quarterback to throw the ball to the tackle. This is used rarely, but can be valuable as a trick play if the defense refuses to guard the tackle.