It seems that just every top GM is now playing the modern interpretation of the Italian Game (with c3 and d3) with an early a2 to a4 Pawn move, something that only a few years back was considered a waste of time in the best of cases. The first "important" game with this idea is, if I am not wrong, the Carlsen - Karjakin game from 2016 World Championship. So what is the point of this early Pawn a2 to a4 move? Just gaining space on the Queenside?
White obviously doesn't want to give light square bishop for knight. He can waste two moves with Bb3-c2, which is the old main line. Or he can just create escape on a2, after which Na5 doesn't make much sense. It gains space while it doesn't have to be so bad to exchange the bishop after Be6, if it didn't make additional moves.
a2-a4 does quite a few things .
- First it makes a Square for the Bishop on a2 .
- Restricts b5 from Black on most occasions .
- a3 move is quite a timid one which looses a tempo even if White decides to play a4 later on.
- Sometimes the Black's Bishop is on b6 where a4 move attacks it.
- a2-a4 marks the beginning of Q-side play from White .
- If you see games of Carlsen and Kasparov they have done Rook uplift to bring the Rook to the K-side .
Besides giving the LSB an escape square on a2, this move is preferred than a2-a3 due to the fact that it discourages the push b7-b5, which is either to sacrifice the pawn and get an open file, or to have some queenside counterplay (usually, the kingside favors White in this opening since he has an extra move).
In addition, a2-a3 is usually played to discourage a Knight or Bishop from using the b4 square, something that is better done via c2-c3 (since it also prepares a central breakthrough).
If you want to keep the bishop on the strong diagonal while slowing down Black's queenside expansion, a2-a4 is definitely a strong choice. However, a2-a3 is probably better if you have a knight on c3 (instead of a pawn) since it keeps off Black from using the strong b4 square.