Whites Bf4 to Bg3 I do not understand

Here we go again, almost the same position and certainly the same opening as the previous time. Again I played this but didn't do the move Bg3 like the computer suggests. Even after 3 hours of thinking at a speed of 5000 KNodes/sec, 48/65 depth, Stockfish still swears by this mysterious Bg3 move and it did so from the start:

I get the obvious challenge of blacks possible ...Nh5 and/or ...Bd6. But despite that it didn't strike as an emergency to play Bg3 at the 9th move already. Am I missing something? Or is it one of those subtleties which only a computer can foresee and is (nearly) useless to human players?

What do you mean "Stockfish swears by it"?

What is the evaluation? Does it rise by more than .003 over the other moves?

You can't use computers to find the best opening moves. 

Just a side note man. That's not the main issue. I'm sure there are alternatives, but the main point is what is Bg3 good for?

very confusing to me

hmmm not sure, Machariel

Two things I never bother to comprehend, are engineers, and grandmasters.

Both seem to be living in their own universe.

@Machariel who played this? Personally I would have thought h3 to allow the bishop access to h2.

Some thoughts:

1. First - there is nothing fast going on in the position, Black is a bit passive, which means its fine for White to play moves that gradually improve the position and you might want to do anyway. In particular there's no need for White to rush to develop the f1 bishop and get castled.

2. One idea of Black which Bg3 stops is Black playing Nh5, forcing the bishop to g3 (white doesn't want to allow an exchange on f4) and then Black playing f5 and then either breaking open with f4 or move the N back to f6 with a gain of space. With the B already on g3, Nh5 can be always be met directly by e.g. Ne5 or cxd5, as Black doesn't really want to exchange on g3 and open up the h-file towards the king.  

3. White might prefer to wait before developing the f1 bishop - otherwise if Black takes on c4 then it could lead to a wasted move.

I don't claim to understand all the subtleties of the move, but lots of positional grandmasters (people like Karpov, Adams, etc) play all these beautiful prophylactic moves where they gradually improve their position and snuff out any chance of counterplay and to my mind this falls into this sort of category.