We so often see strong players sacrifice pawns or pieces in exchange for activity. Pieces that are active control space, create threats, and force the opponent to respond. The player whose pieces are active has the initative and is the one dictating the course of the game. Let's look at a game in Tata Steel Chess to illustrate this point. The game was played by 14 year old Yaz Erdogmus and rank 30th in the Fide live ratings, Vladimir Fedoseev.
The game started with 1. e4 e5 2. Nf3 Nf6 3. Nxe5 d6 4. Nf3 Nxe4 5. d4 d5 6. Bd3 Bd6 7. O-O O-O 8. c4 c6
The Petroff Defense, it has a reputation of being drawish. 9. Re1 Re8 10. Qb3 Na6 11. a3
Not a usual move in this position. It simply denies the b4 square from Black's Knight. 11. ...h6 12. Nbd2 Nf6 13. Rxe8+ Qxe8 14. c5 Bc7
Already Black's Queen side is cramped. He has still has pieces on their original squares and stepping on each other's toes. 15. Nf1 Nb8
An unfortunate retreat to try and find better squares. 16. Ng3 Ne4 17. Nh5 Bd8?!
Gives up control of the h2-b8 diagonal. I would prefer Nbd7 to activate the Knight. 18. Bf4 g5? 19. Bc7?!
Distracting the Bishop from defending the f6 square. 19. ...Bxc7 20. Bxe4 Nd7? 21. Bf5 Qd8 22. Re1 Kh8?! 23. Qe3 Nf8
The pieces are equal but White's activity gives him a decisive advantage. Every move now comes with a threat and Black is forced to respond. 24. Ne5
Bxe5 Qxe5+ loses. 24. ...Qe7 25. Bxc8 Rxc8 26. Qh3
Now threatening to capture the Rook. 26. ...Re8 27. Ng3
White doesn't give Black a rest. Now threatening Qxh6+. Black's moves are forced. 27. ...Kh7 28. Nf5
Again forcing Black's hand to defend. 28. ...Qe6?! 29. Re3
Moving the Rook to the third rank while threatening a discovered attack on Black's Queen with Ng4. 29. ...Qf6 30. Nxh6
A nice way to finish the game with a Knight sacrifice. 30. ...Qxh6 31. Qf5+
So many ways to win in this position. 31. ...Ng6 32. Qxf7+ Qg7 33. Qxe8 Bxe5 34. Rh3+ Nh4 35. dxe5 Kh6 36. g3 Qh7 37. Qe6+ Kh5? 38. g4# 1-0
Finally, the game ended in a mate and with a pawn delivering it. Nice sportsmanship by Fedoseev to allow mate.
The following game illustrated the importance of activity. The material was equal at some point but White's activity spelled the difference. He dictated the game with many threats while improving the position of his pieces while Black was forced to respond to each threat.
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