The 'punter' is the player that kicks the ball away to the opposing team when the offense fails to get a first down. While punter is generally not a position that is included in fantasy football league commissioners can elect to change the settings to include punters.
REMEMBER: AYP = average yards per punt, which is the average distance traveled of the player's total punts throughout the game
Since solid, consistent punters are much more common than reliable fantasy performers at 'skill positions' (quarterback, running back wide receiver), it is best to wait until the later rounds of the draft to select a punter.
One important strategy when deciding which punter to draft is to examine the offense of the team the punter is a member of. The NFL's best offenses tend to score touchdowns or field goals on most of their possessions, negating the need for a punt. Therefore, the best fantasy football punters tend to reside on teams that have difficulty gaining yards and find themselves kicking the ball away to the opposing team rather frequently.
Including the punter position can be a fun way to switch things up when it comes to fantasy football. It gives team owners who might not be adept at drafting other positions (i.e. running back, wide receiver). Including punters in fantasy leagues also adds excitement to an otherwise boring portion of real-life games, giving fantasy managers a reason to celebrate a strong punt.