The en passant rule was put in after the rules had been changed to allow the pawn to go forward 2 squares on it's first turn. The new pawn move had one bad side effect: it gave the player who was under attack the opportunity to lock the pawn formation by puching past the attacking pawn on an ajacent file. The result was sometimes a totally interlocked pawn formation with no opportunities for attck by either side. This was dull. The en passant rule was a little tweak to the rules that made it a bit tougher for the defender to lock up the pawn formation, and it worked very well.
As to why the rule is in effect for only the next turn, I would have thought that was obvious. The advancing pawn in only available of that third rank square for one turn. After that, it is securely on the fourth rank. These is no situation is chess where you can go and capture a piece on the square it used to be on!
This is the correct answer. Saying that the rule is the way it is because of its name is nonsense though.
Lol it's as if people assume there was just a pressing need for a rule named "en passant" and picked a move that best fit the term.