Knowing how to win or draw a rook-and-pawn vs rook ending is one of the cornerstones of endgame knowledge.
In my 3.4 million game database, approximately 20% of the games result in this ending, and there are probably more games where the Grandmasters resign or agree to a draw because a transposition to the ending is unavoidable.
If you know these endings, then you can play better middlegames, because you will know when it's good to trade into one, and when you should avoid doing so.
It will also improve the quality of your rook play in general, I think.
I thought about reproducing the theory here on the site, but the wikipedia entries are so good that it makes no sense to "reinvent the wheel".
For those who are learning chess, or for anyone not already familiar, I consider this essential study.
The Lucena position shows how the side with the pawn wins the game, while the Philidor position shows how to draw when the other side has the pawn. Here are the links: