Please explain why this is not checkmate?

I thought I was getting the hang of checkmate, but just played this game and thought black had checkmated white. 

My thinking was that whites king could not move from this position and is therefore checkmate.

Could anyone please explain what I am misunderstanding here? 

Thanks.

Fen: 8/8/8/8/2R5/6kp/5q2/5n1K w - - 0 1

This is not checkmate because the White King is not in check. If it were to have no moves AND be in check then that would be checkmate. This position would be Stalemate (drawn) if the White Rook wasn't on the board because then White would have no legal moves and the game would be a draw.

There are jokes about this because one side could be up a ton of material and draw the game by Stalemate if they aren't careful. Checkmate must also put the King in check.

Ah ok thanks for that, is this essentially because white king still has a legal move of h2? 

The White King can't go to h2 in the first position. The Black Queen controls this square.

The part I am struggling to understand though is why the white king is not in check in that position? Wherever white king moves it would be at threat of capture? It sounds like the part I am misunderstanding is 'being in check'?

The problem is that your opponent's king is not in check right now. The king would be threatened if he moved, but that's okay because he is not threatened where he is currently. You have to make a move that makes sure that he is in check and cannot move anywhere else.

Thanks for that, I think that has cleared it up and where I was going wrong. I was thinking just because white king is not able to move anywhere legally, it is in check. But actually then, as long as the white king is not being FORCED to move (still have other pieces available that can move around) then it is not check. If black queen moves to g2, THEN it is in check and therefore checkmate.

One additional point is that many people think that stalemate is merely when the king cannot make a legal move but is not in check (though showing people the starting position seems to get them to understand the correct rule).  Your post highlights that there must not be any legal move by any piece, not just the king, and the White Rook's ability to make means it is not (yet) a stalemate, though Rg4+ Kxg4 would  be a stalemate and Rg4+ Kf3, Rf4+ Kxf4 would also be a stalemate and Rg4+ Kf3, Rf4+ KanyOther, Rxf2 Kxf2 is also a stalemate and if the king does not recapture the K+R vs K+N+P endgame is also fine for White.

Both these definitions are wrong. (Edit - Hah! You deleted this post while I was replying to it. Good, you probably just replied too quickly and realized your mistake.)

Check is when a piece or pawn of one color could capture the king of the opposing color on its next turn.

1. If it is the king's turn to move, then that side must make a move to relieve the check. If they have no move to relieve the check, then it is checkmate. Relieving the check doesn't have to be a king move! Any move by any piece or pawn on that side can relieve the check: capture the checking piece, interpose between the checking piece and the king, or king flees.
2. If it is not the king's turn to move, then it is an illegal position. The king cannot be captured! The king's side must take back it's last move, which was an illegal move. Then they must make a different move, one which does relieve the check (if they have one).

I can't understand why you got a thumb-up for that post. Check is about whether or not the king is being attacked by an enemy piece or pawn, and checkmate is about whether the king's army has any way to stop the attack by the enemy piece or pawn.

Checkmate is a check which cannot be escaped.  There is no check in that position, therefore no checkmate.

It is a very interesting position, because at first glance it appears that black is in control, but it's actually white who is in control, with the ability to invoke a stalemate with Rg4 check.

If black captures the rook, it's an instant stalemate. If black moves the king to f3 to escape the check, white can check again with Rf4.  Black's only option to avoid stalemate is to keep moving the king out of the way without capturing the rook, but that leads to white eating the queen and knight which ultimately is a win for white.

looks like others have answered by now, but yeah the original position isn't checkmate because the white King isn't attacked by any black pieces (in check).

Because the white king doesn't in check, nowhere to move. If it is checkmate, black Queen must be g2 or h2. well, move to queen f2 is a great mistake....

Every piece except the pawn controls h2

No, because pinned pieces can give check too.

Just keep it simple, the guy is obviously a beginner.

Check means the king is under attack.

In a stalemate, the stalemated side has no legal moves to make - if the king moves, he would have to move to an attacked square, but he is not currently in check.

In the original position, the White king appears unable to move, but the White rook can.

If White makes a move like Rg4+ (like jetoba has noted), Black is in for an issue.

If it's Black to move instead, Black plays Qg2# giving check to the already paralysed king (all because the White rook is present, thereby preventing a stalemate)

It's not even a stalemate at all. Look carefully.

Fun fact: the simplest google search often helps with these things (for example, "weird pawn move" gives en passant immediately), but this time it fails. Searching for "check" gives a lot of irrelevant results (i. e.  A check is a written, dated, and signed instrument that directs a bank to pay a specific sum of money to the bearer). You need to search for "check chess" or something like it.

My mistake didn't see rook