Can someone explain this best move to me

Eidt: I still don't understand this puzzle does anyone want to try it?

Here is a pratice puzzle I was doing.

http://www.thechesswebsite.com/bestmove10/

It says the best move is d4 to d5. And says white will win material. But how?

I know the black knight can't move right now. But after whites move black can capture with his pawn with the move e6 captures d5.

If white goes c3 to d5 to capture black can take back with d8 to d5.

No matter what white will lose material with this move. What am I missing?

Hi, I think the point is after d5, xd5: Bg5! Threatening to remove the defender. Without d5 and xd5 black could play g6 as a response to Bg5, but after this exchange this is not possible because of Rxe7 Nxe7 and Bxf6. It's tricky, and a little vague for a chess puzzle in my opninion, but after Bg5 black will have to give material (Ne4?!) to avoid mate. I understand your doubts, hope this helps. Cheers

Your not missing anything..there is a h7 mate, but d5 and e6 capture is safe.This is what we use too call "cooking a puzzle"(defeating it)

I think I see what you mean, but for black after Rxe7, instead of Nxe7 why not take the rook with his queen while still defending his knight?

After Qxe7 white has Nxd5, forking the queen and the pinned knight. 

Some might disagree with that. Glad to help 

I'm still having trouble. After the situation vinfish pointed out why can't black still defend checkmate the same way? 

Like this

Whites move Bg5,   Black g6,   white Rxe,   black Nxe7,    white Bxf6,

At this point I do not see a quick checkmate because of blacks move of g6. And white is down a rook and a pawn. Black is down a knight and a bishop. So they are both down 6 points.

The answer says white will win material. 

Any help would be appreciated

The position after 1 d5 ed 2 Bg5 g6 3 Rxe7 Nxe7 4 Bxf6, although in theory even in material, isn't really equal.  White has a substantial pull because 2 pieces are worth quite a bit more than a rook and pawn in that position (as they are in most middlegames).  Factor into that as well Black's weakened kingside and his lame bishop (blocked by a pawn) and White is doing very well indeed there.

I must say though that the problem was badly worded...and it's absurd to just post the single move 1 d5 and expect it to "explain itself," as it were.