At a glance...
Be5 threatens mate.
That's why.
You're 1600 so that should be enough of a hint.
the immediate threat to White is Bc5
Oh, now I see you're rated more like 1000... so not knowing chess notation makes sense (Bc5 is an illegal move).
Ok, so you need someone to give you more help.
The answer is moving the f pawn(s) will let the c2 rook defend the h2 pawn.
I think I see ...
c2 Be5
f4 Bxf4
f3
This lets the Rook now on c2 to have line-of-sight to the h2 pawn.
Yes?
What should White do then?
After that white should resign, because he's a bunch of material down.
But if you want to know how an engine would play it, you can use the chess.com analysis board to play moves against the chess.com engine and find out for yourself.
Be5 is forced mate In 2 I think
From the move White did play, yes Black won in three moves.
Be5
f4 Bxf4
f3 Qxh2#
I think it was partly the fact that Black did move the pawns in the actual game for no effect is what made it hard for me to understand the earlier Rc2 move and llama47's hint - the pawns had moved and hadn't worked so I didn't immediately see why moving them following Rc2 would now help. If that makes sense?
Incidentally, the computer analyses of White's final move; instead of f3, it recommends Qh5 which leads to Black Qxh5 and just delays the Checkmate as far as I can see. So looking over the game, I saw this moment as the last chance to avoid Checkmate, I would have done so differently and didn't understand Rc2 at first.
While I do accept that White's move here is a Blunder, I cannot understand the move the computer is saying is "Best". In fact, I don't see how it helps in any way at all and to my (admittedly feeble) Chess Brain, it's no more helpful than the move White did make and the computer says is a Blunder.
Surely the immediate threat to White is Be5 and the threatened Checkmate. So White either needs to stop Be5 with their next move or find a way to avoid the Checkmate the turn after.