This is the Philidor position. It is one of the rather important rook endings that you need to know. The Lucena position is another one, but there's another article on it already.
So here is the basics:
It looks like white is going to win here, but he can't. Black has a rook on the 6th rank, and the king can't get by. So white can wait and wait...he has the extra pawn, better king position but he can't win. So he'll get frustrated and advance the pawn.
Yikes! Now he can march his king up with pawn protection...or not.
The refutation of that is Rh1! Black can now attack white with checks so that white can't promote.
This is an important rook ending position. It is crucial, and can save tons of lost-looking endings, like this one that I played in a recent tournament:
I exchanged off 2 pawns, and easily got a draw, although my opponent wasn't that happy...
Here is the WRONG way to try to defend against white in the Philidor:
Here white wins easily with Rh7, swinging the rook to the other side. Its an important maneuver. That's why passive defense doesn't work here.
So summing up, in the Philidor, black should:
1.Keep an active rook on the 6th rank cutting the king off
2.Just sit around
3. Wait till white gets bored and advances his pawn
4. Go to the 1st rank and start checking
5. Offer a draw and it'll be accepted.
Black should avoid passive rook positions though.
Thanks for reading!