White has the first move, and therefore a significant initiative. White wins 10% more often than Black simply on the power of that initiative. It is important not to squander the opening advantage with a move that does nothing.
White chooses an excellent move, common among beginners and experts alike. The move has several advantages.
This move for Black is good for the same reasons listed above. Note that the two e-file pawns are not threatening to capture each other, because pawns capture diagonally. Instead they merely block each other until something breaks the logjam.
White makes another fine move. He is mobilizing his forces by bringing a knight forward into attack position. Black's pawn on e5 is now in danger.
White could have moved out his queen instead, but that would be dangerous. The queen is too valuable to trade for any other piece, so it can't do much by itself unless the opponent carelessly leaves pieces unprotected. It is better to wait until there are other pieces in the fray which can serve as shock troops for her highness.
White also could have moved out his light-squared bishop. That would not be a bad idea, but it isn't clear yet whether the bishop wants to be at c4, b5, or possibly even behind the pawns. The knight, on the other hand, usually goes to f3 anyway, because the other squares it could move to are inferior. On h3 it would not attack the center, and on e2 it would be temporarily in the way.
Black makes a worthless move. He needed to defend his pawn with 2...Nc6 or counter-attack White's pawn with 2...Nf6. Either knight move would maintain the balance of the game by contesting the center.
The move 2...f6 appears to defend the threatened e-pawn, but this is an illusion, as the game shall demonstrate. Black has weakened his kingside, allowing attacks on the f7 square, which is protected by nothing other than the king itself.
White attacks immediately, sacrificing his knight for two pawns, although generally White would need three pawns for the knight to have material equality. Although White can't calculate far enough ahead to know exactly how his sacrifice will pay off, he judges that his attack will be at least strong enough to compensate.
Black makes the only move consistent with his previous plan, but it is not best. The best try for an equal game was 3...Qe7, skewering White's knight, pawn, and king. That is to say, the queen would indirectly be attacking everything in the e-file. After the knight moves away, the queen can take on e4 with check, safely regaining the pawn.
Retaking the knight now merely invites White's queen to jump into the fray with check. The fact that Black cannot afford to take the knight shows that 2...f6 did not really protect the pawn at all.
The game's first check! There are three legal ways to respond to check:
This move leaves Black in a dangerous position, because his king is so exposed. Furthermore, his rooks, bishops, and queen still have no way to get out. The Black position is no more developed than it was at the start of the game.
Another check. Black now has only one legal move. He can't interpose anything between the king and queen, and he can't take the queen, so he must move his king out of check. There is only one square next to Black's king which White's queen is not attacking.
White's queen is a dangerous attacker. However, because it is too valuable to trade for anything, it can only take undefended pieces. Everything in Black's camp is defended by something, so the queen has done all it can do by herself. It is time to bring in reinforcements.
This is an excellent move to keep the pressure on Black. Because it develops a piece and gives check, White prevents Black from consolidating.
If White played less energetically with 6.Nc3, his advantage would evaporate instantly. Black could answer with 6...Be7, giving the king room to retreat to f8. Once Black gets his king to safety, he might actually be winning. White has only two pawns for the sacrificed knight, which leaves White at a material disadvantage.
Black makes an excellent defensive move. Never forget that moving the king isn't the only way to get out of check!
Admittedly, Black's d-pawn is a dead duck. It is attacked by White's bishop, queen, and pawn, three times altogether, while it is defended only once, by Black's queen. The sacrifice is worthwhile, though, to open up lines for the queen and bishop so they can help with the defense. Now if White fails to find the best continuation, Black has some chance to counter-attack.
White gives check yet again, which prevents Black from doing anything constructive. Let's review the three ways to get out of check:
Now White must think of a way to continue the attack. He would like to play 8.Qf5+, driving Black's king to h6 where it can be cornered and checkmated, but Black's c8 bishop is guarding the square f5. If Black hadn't interposed with 6...d5, he would now be subject to a forced checkmate. As it stands White has to be more creative to keep the initiative.
Again White finds a strong continuation. White is threatening to force the Black king to h6 after all with h5+. Also the pawn protects the g5 square which is important in some mating combinations. Finally, there is some chance the rook will be able to join the attack down the h-file.
Black plays a tenacious defense in a precarious situation. White's pawn is blocked from further advances, and the king has a new escape square on h7. Black's position is still precarious, but there is no immediate way for White to force checkmate.
Now let us take a step deeper into chess reasoning. White knows Black is on the run for the moment, but if he has a chance to regroup, the game is far from over. Three pawns for the sacrificed knight is roughly material equality.
If White brings additional forces forward with 9.Nc3 or 9.d4, the obvious developing moves, Black will harass White's queen with 9...Bd6. That would force White to lose time protecting the queen. Black would gain time to get his pieces out and get his king to safety.
White desperately wants a quick kill, but can't see how to get it. He is annoyed that Black's bishop on c8 prevents him from playing 9.Qf5+ and administering the coup de grace. Therefore he asks himself, "What if Black's bishop were not on c8? If only that annoyance were removed, I could do great things."
White finds a forceful continuation that puts Black in dire straits. Black's best bet now is to ignore White's bishop and harass White's queen with 9...Bd6, but then White calmly plays 10.Qa5, maintaining the threat on f5 and forcing Black to lose material. One possible line of play is 9...Bd6, 10.Qa5 Nc6, 11.Bxc6 Rb8. The checkmate has been avoided, but now White has a large material advantage (four extra pawns) and can win slowly and surely with patient developing moves like 12.Nc3.
As it happens, Black does not understand the danger. He grabs the bishop for a material advantage of his own (bishop plus knight versus four pawns) and suffers the consequences.
The crushing move can be unleashed at last. Black has only one legal reply.
White continues the attack with a special kind of check, the discovered check. He moves a pawn, but it isn't the pawn which gives check. It is White's bishop, attacking from its home square, which delivers the blow.
Note that Black's king has no legal moves, and White's bishop is safe from capture, so interposition is the only option.
At this point White has an easy win with 12.Bxg5+ Kg7 13.Bxd8. The material advantage of a queen and five pawns for a bishop and a knight is overwhelming. However, weak players have been known to play on in completely hopeless positions rather than resign. In order to forestall a long, boring mop-up operation, White looks for a direct kill.
Truly a masterful move! White doesn't even call check, but mate is now inevitable.
Nothing can save Black short of White forgetting his plan, but there is some logic to Black's move. Where can White's queen go? Any of Black's pieces it could take is protected. If White trades queens, then the attack is over, and Black is winning. Finally, if White's queen simply retreats, Black will strike back with a check of his own: 13...Qxe4+!
But White must have foreseen this possibility, or he would never have played 12.Qf7 instead of 12.Bxg5+.
Black can't get out of this check by interpostion or by moving the king away. All retreat is cut off by White's well-placed queen. The only option is to capture the checking piece.
Checkmate. Black can't interpose anything, because the rook is giving check from an adjacent square. Black's king can't move away, because White's queen covers all retreat squares. Black's king can't capture the rook, because then it would be in check from White's queen. Finally, Black's queen can't capture White's rook because it is pinned. If it moved away, White's bishop on c1 would be giving check to Black's king.
Notice that, although material considerations are very important in chess thinking, one doesn't win by having the most pieces. One wins by delivering checkmate. White was behind in material almost the entire game, including in the final position, but came away with the victory nonetheless.