Why a4 in this position?

Below is a screenshot from my analysis of a game played with a King’s Gambit opening. The computer suggests that the best move in this position, which I missed, was pawn to a4.

Could someone explain the value of playing a4 in this position?

I suspect the idea is to threaten the capture of the bishop. However, it seems to me that Black can simply respond with a6 and retreat to a7, neutralizing the threat. Wouldn’t I just end up wasting multiple tempi in the process?

Thank you in advance!

I'm not sure why it's not showing. I uploaded it again, in a response section. Please advise if it's visible. If not, I'll input the PGN.

Takes space and threatens a5

I see your screen-shot. I'm on a PC though.

Why a4? To harass the Black Bishop. It also seems to force Black to reply with a Pawn move (a6 or a5), so no time is really lost.

I doubt that I would have played it. Humans look at chess positions differently than computers do, so you can't expect a Human to tell you what "the idea" of a computer's move is. Computers don't make moves based on ideas. They make moves based on brute-force calculations.

Ok, first of all, let's evaluate this position before a4.

White has the move and he is at the moment a pawn down but can easily win back the pawn on the next move. He has 3 minor pieces out, while black has only 1 plus a queen.

So, it is clear that after the most straightforward move Bxf4, white has the advantage as he would now have 4 pieces out compared to black's one plus a queen. This is an easy move to make.

As for the engine evaluation, for me the engine shows 0-0 as the best, Bxf4 as the second best and a4 as a very close third best. But all three are completely fine. Edit: After I wait for a minute or 2, a4 is the best, but only slightly.

The idea of Bxf4 is clear, develop and regain the pawn, maintaining opening advantage. 
The idea of a4 is actually like an intermezzo move. You play a4 to provoke a pawn move on the queenside to save the bishop (a6, a5 or c6) and then to play Bxf4 or 0-0 (perhaps even to insert a5 if you wish, though after c6, you shouldn't as he might play Bc2 and perhaps keep this pawn, at least for a while).

What does a4 does? It just gains some space, it is a free move. It certainly is not necessary, but you can if you want to.

The point of 0-0 is to show readiness to even sacrifice a pawn and allow the opponent to defend it at the cost of another tempo.

So basically white has a choice to play Bxf4 or 0-0, and another choice to include a4 before one of those moves or not.

Personally, I would probably just recapture the pawn and go for the safe advantage, but I am sure many sharper players would play 0-0 and try to dare black to spend a tempo defending that pawn. Would I play a4 before that? I am not sure, but it is to some extent a logical move to insert.

That was very helpful feedback. I really appreciate you for the thorough response. Thank you!

You're welcome.