[FEN "5rk/Q1p2p1p/4p1p/2Pq2b/3P2n/4P1Pb/PP1B1P1P/R2R2K w - - 0 1"]
Apparently, the system says that it's checkmate, but I don't get it. Can someone please explain it?
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This isn't checkmate yet. Neither side is even in check!
However, black is threatening to play Qg2, which would put white in check and there would be nothing to stop that check -- checkmate.
So it's not checkmate yet, but it will be soon unless white defends against the threat somehow.
And there is no way to defend against it -- white can block the queen's path by putting a pawn on e4 or f3, but black's queen will just take those pawns and then the threat will be renewed.
I believe you are looking at an engine, and it's telling you is that black, with the correct play, will checkmate the opponent. It's not checkmate yet, but as the game progresses, white cannot stop checkmate. The engine is showing checkmate not because it's checkmate, but because black will eventually lead to checkmate. White can delay the game by giving up material, but eventually white will run out of defenders, and black will mate. If you look at either side, they both have moves! Stalemate leads to draw, where the side that is going to move does not have any legal moves, but that's not the case here.
tldr: both sides have legal moves so it's not stalemate, and black, with the correct play (not making any dumb moves like Qxc5), will eventually checkmate white, as there is nothing white can do to stop it.
This is a simple question that deserves a simple answer: This position is neither checkmate or stalemate.
Checkmate is where the player to move has no legal moves and is in check. Stalemate is where the player to move has no legal moves and is not in check. In this position, either player would have legal moves if it was their turn, so neither definition applies. (The White king has no legal moves, but other White pieces do have legal moves.)
Now we look specifically at checkmate. The definition is normally stated the other way around: The player to move is in check and has no legal moves. But neither player is in check, again showing that the position is not checkmate.
However, this position is a forced mate, either a mate in one (Black to move) or a mate in six for Black (White to move). This means that:
This just means that Black can reach checkmate in the specified number of moves, if they choose the right moves; if they choose different moves, they may take longer to reach checkmate, or not reach it at all.
While other answers have confirmed that this position will lead to a checkmate by Black, I want to answer the second part of your question (as per the title), the stalemate.
A stalemate occurs when a player is not in a checked position, but has no legal moves to play. An example would be the following position, with Black to play.
[FEN "R4n1k/6R1/p7/Pp6/1P6/2B5/5K2/8 b - - 0 1"] [StartFlipped "0"]
Black can't move either pawn, since there's a white pawn in the way.
Black can't move the knight, since that would put the King in check from the white rook on A8.
And Black can't move their King, since they would move into a check (either by the rook or by the bishop).
Yet Black's King isn't in check, so it isn't a checkmate.
Also note that were it White to move, it wouldn't be a stalemate. White could capture the knight with the rook, which would be a checkmate, or White could capture Black's A-pawn with that rook, with would allow Black to move the knight, since this would no longer put Black's King in check.
A stalemate is a draw, but keep in mind that not every draw is a stalemate. (Maybe that was why you called it a possible stalemate?)