user8390: 
This is a position from a game between Fischer and Ibrahimglu, 1970.
Black's last move was 11. ... Qc7 from d8. According to Stockfish (depth = 28), 12. a4 is the best move for White. The other recommended moves are Nb3 and Rd1. But a4 seems to be better than Nb3 by more than 0.1 point.
It seems to be a very logical move as Fischer played it too. Only the logic behind it is out of my (an intermediate player) reach. :)
The game continued with 12. ... Rad8 13. Nb3 b6 14. Be3 c5... Fischer went on winning this game.

user7500: 1. a4 allows White to place his knight on the c4-square without having to worry about ...b5 kicking it away because that would be too weakening for Black, because it would make the a-pawn backwards on an open file.
1. a4 also gains space and opens the possibility of a5-a6 to soften the Black queenside for the g2-bishop. If black stops this with ...a6 or ...a5, then Black will have a hole on b6.
A knight on c4 would allow white to move his bishop to f4 to attack the black queen. If Black responds ...e5, this creates a permanent weakness on d6, and White can put his knight there. ...e5 also blocks Black's bishop. The knight on c4 also takes away many squares from the black queen, so if Black does not want to weaken with ...e5, the black queen will have to go to an inactive square.

8390: <p><a href="https://i.stack.imgur.com/GB1Qr.jpg" rel="noreferrer"><img src="https://i.stack.imgur.com/GB1Qr.jpg" alt="enter image description here"></a></p>

<p>This is a position from a game between Fischer and Ibrahimglu, 1970.</p>

<p>Black's last move was 11. ... Qc7 from d8. According to Stockfish (depth = 28), 12. a4 is the best move for White. The other recommended moves are Nb3 and Rd1. But a4 seems to be better than Nb3 by more than 0.1 point.</p>

<p>It seems to be a very logical move as Fischer played it too. Only the logic behind it is out of my (an intermediate player) reach. :)</p>

<p>The game continued with 12. ... Rad8 13. Nb3 b6 14. Be3 c5... Fischer went on winning this game.</p>
 7500: <p><code>1. a4</code> allows White to place his knight on the c4-square without having to worry about <code>...b5</code> kicking it away because that would be too weakening for Black, because it would make the a-pawn backwards on an open file.</p>

<p><code>1. a4</code> also gains space and opens the possibility of <code>a5-a6</code> to soften the Black queenside for the g2-bishop. If black stops this with <code>...a6</code> or <code>...a5</code>, then Black will have a hole on b6.</p>

<p>A knight on c4 would allow white to move his bishop to f4 to attack the black queen. If Black responds <code>...e5</code>, this creates a permanent weakness on d6, and White can put his knight there. <code>...e5</code> also blocks Black's bishop. The knight on c4 also takes away many squares from the black queen, so if Black does not want to weaken with ...e5, the black queen will have to go to an inactive square.</p>
