White’s bishop on d3 is pointing at h7. The knight on f3 can reach g5 in one hop. The queen on d1 has the d1 to h5 diagonal free the moment that knight moves. And Black has no knight on f6. That is the whole shopping list, and it means Bxh7+ works.
7 
2 
a 
d f 
g The three moves
1.Bxh7+ Kxh7 2.Ng5+ and the king has to choose. Back to g8 is the usual answer, and then 3.Qh5 arrives with the threat of 4.Qh7 mate, the queen protected by the knight on g5.
Black gives the king a square with 3…Rfe8, and the queen walks straight in: 4.Qxf7+ Kh8 5.Qh5+ Kg8 6.Qh7+ Kf8 7.Qh8+ Ke7 8.Qxg7 mate. Play it out on a board once. Every black move in that line is the only legal one, which is what a beginner never quite believes until the pieces are in front of them.
The name is a joke about the horse the Greeks left outside Troy: a present you should have looked at more carefully. What Black is really walking into is a mating net, built with three pieces and one wrecked pawn shelter.
The five conditions
Before you spend the bishop, check all five. A bishop bearing on h7. A knight that can reach g5 with tempo. A queen with a clear road to h5 (or to h4 via d1 to h5, or a rook lift). No black knight on f6 and no black pawn able to cover h5. And a black king on g8 with pawns still on f7 and g7, so it cannot run to f8 and away.
Miss one and the sacrifice is usually just a bishop for a pawn. Get all five and you often have mate by force, or the queen collects f7 and g7 and the game is over anyway.
Stopping one
The defence is not clever, it is early. Keep a knight on f6 while your opponent’s light bishop is aimed at h7, and think twice before pushing a pawn to e5 yourself if that means your f6 knight has to leave. If you have already played …h6, the sacrifice becomes Bxh6, so the same rules apply one square along.
And if the bishop lands anyway, take it. Refusing usually loses to the follow-up rather than to the sacrifice. Then run: h7 to g8, and if the queen never gets to h5, you are a piece up.
For a hundred more of the same picture from the attacking side, work through the kingside attack puzzles; most of them are this pattern with the furniture rearranged.