fredthebear: This game finishes with some simple but powerful tactical concepts on the last move 41...Bb2! Tactics are more than just sampling possible moves. Don't just look here and there and hope to stumble onto something. Identify which units are under attack, and if they are defended sufficiently.
(Pawns often make for the best defenders, because they are slow, less valuable, and don't have anything better to do. Get your minor pieces out ahead of your pawns, or between your pawns. Pieces want the freedom to fly around the chessboard instead of sitting at home on passive guard duty. Pawns don't mind sitting still because they can't fly anyway.)
On the final move of the game, Black moves a threatened piece (the dark-squared bishop) to relieve the queen of her defensive duties. The great Australian chess writer C.J.S. Purdy refers to this as an "Untie", a necessity similar to getting out of a pin. An Untie is a release of one's stale defensive duties, and gaining increased mobility. It's like the last bell of the day releasing the schoolkids to charge out the doors to their own pursuits! There are no more restrictions -- they can go hither and yonder. In this case, the bishop move means the bishop is no longer being threatened with capture by the rook, so the queen is given freedom to roam as she chooses. The queen has been untied!
Black moves the threatened piece by making a threat of it's own; the bishop forms a battery with the queen (what I refer to as a "spearhead"). In this case, the spearhead threatens a double attack on the White knight and cornered rook. Both the knight and rook are defended once, but now attacked twice. This is a case of White being "outnumbered."
Correct counting is an unappreciated tactic. Study Dan Heisman's writings to learn more about this. Where there is one defender protecting a defendant against one attacker -- DANGER LURKS! Simply add an attacker to increase the count (or subtract the defender) to a numerical advantage. Mathematically, adding an attacker could be written as (1 vs. 1+1, the same as 1 < 2). Subtracting a defender is written as (1-1 vs. 1, the same as 0 < 1).
Expanded chess terminology refers to this challenge against a defender as Undermining, Overloading, Removing the Defender, Interference, etc. in many different forms. That's way too much to cover here. Let's take a short cut... An easy way to talk to yourself is to say "aim one of my unit at/through two of his" as well as "aim two of my units at/through one of his."
Of course, your opponent is trying to outnumber you on a certain penetrating square as well. Turn about is fair play! So pay attention to what his aggressive plans aim at in your own army's camp! In the beginning of a game, the advanced pawns in the center come under fire like this. You try to protect your advanced pawns with defenders while threatening his advanced pawns with attackers.
When the bishop takes aim at the cornered rook with 41...Bb2!, it is a matter of "attacking (taking aim at) a more important piece." Checkmate is the highest form of attacking a more important piece. When studying the games of the great Paul Morphy, you will notice that if Morphy could not attack the opposing king, he would often target the opposing queen, the next most important piece. Here, the bishop (a minor piece) is attacking the more valuable rook (a major piece).
Finally, as you can see, Black's last move had more than one purpose. In this case, Black relieved the queen of her defensive duty, the bishop came off the edge of the board and formed a battery on the long diagonal, and made a double attack against two White pieces which only had one defender each. Most good moves on the chessboard have more than one purpose, and suggest a follow-up move.
White resigned knowing he was going to lose a piece on the next turn. He could not move both the knight and rook to safety at once, nor counter with a forcing check, capture or pawn promotion of his own.