An eligible receiver in football is a player that can legally catch a forward pass from the quarterback. Eligible receivers line up one yard off the line of scrimmage or are the furthest outside player on the line of scrimmage on their side of the field.
To remain an eligible receiver must also be sure to not travel out of bounds. Stepping out of bounds voluntarily will earn make you ineligible for the rest of the play. Being pushed out of bounds requires the receiver to get back into bounds immediately to remain eligible.
Wearing the numbers 50-79 will also make a player ineligible if he does not announce it to an official prior to the play. NFL Rulebook
The line of scrimmage and eligibility
Players who line up on the line of scrimmage are usually going to be ineligible. Only the player on the leftmost end of the line and the rightmost end of the line are going to be eligible receivers.
On any given play a team will generally have seven players on the line of scrimmage. The players on the line scrimmage are usually offensive linemen.
If all players were eligible for every play there would be too many potential receivers for the defense to cover.
This is why you will see slot receivers, running backs, and tight ends often line up one yard off the line of scrimmage. These players are not usually on the outside of the formation which means they need to be off the line of scrimmage to remain eligible.
Staying In Bounds
Staying in bounds is another way a player can remain an eligible receiver. When running a route a player can not step out of bounds voluntarily or he will become ineligible.
If the player steps out on his own he will not be able to become eligible by reestablishing himself in bounds. When this happens the official will often throw their hat to show that the player is ineligible.
If a player steps out of bounds due to being forced out they have a chance to become eligible again. If the play re-establishes himself by placing a body part inbound aside from his hands he will then become an eligible receiver again.
Jerseys numbered 50-79
Players that have jerseys numbers between 50 and 79 are going to have a harder time being eligible receivers.
Have you ever been watching a football game and heard the official announcement that a player with a specific jersey number is now eligible?
This is because this rule regarding eligible receivers and jersey numbers.
To give the defense an easier time determining which players need to be covered the common numbers of offensive linemen are declared ineligible.
If a unique formation is used one of these players may end up on the end of the line of scrimmage. This would then allow them to be an eligible receivers. The team must then tell the official who will announce it to the defense.
This way the defense knows that a player wearing an offensive lineman number may need to be watched in pass coverage. If the player is not announced by the official then players with this jersey number remain ineligible.