Ideas can vary a little depending on the exact position, but in general the primary idea is just to hack at Black's king. If Black takes the pawn and then castles kingside, there's obviously going to be a huge attack.  If Black doesn't take the pawn but still castles kingside, then White can drive the knight away with g4-g5, which can be a prelude to another form of attack, sometimes with h2-h4-h5 and opening lines against Black's king by means of pushing one or both of those pains to the 6th rank. 

Notice that White isn't always really sacrificing the g-pawn anyway, since often Black's pawn on g7 is undefended and x. Rg1 Nf6 y. Rxg7 regains it.  Also notice that in many of these positions, White can manage to castle queenside without much trouble, but Black cannot, so if he chooses not to castle on the kingside, then his king is often left in the center for a while. 

Finally even if Black plays well and doesn't come under direct attack, White hopes that g4-g5 (or the threat of it) deprives the knight of its best square, causing congestion and confusing in the Black ranks.  The space he's gained can also be beneficial much later, such as happens when White plays his pawn to h5 in the Caro-Kann. 

Yeah even in the sicilian I don't get it that much. I just assumed that if White played g4 that no one was going to actually castle on that side... I've seen it in similar queen's pawn games but I really don't understand it. I see g4 and I think, "attack" but then there is no attack and then I wonder what the point of it all was. 



I just have a hard time seeing what you gain from playing this move unless there's some tactical point to it.

Continuing from RdC, there is also the famous g4 in the Phillidor, popularised by Alexei Shirov and also the g4 in the Botvirnnik Semi-Slav also popularised by Shirov but I think Shirov said it was invented by his friend, GM Shabalov, now US formerly Latvian.
Have a look at Shirov's Fire on Board vol 1 and also Shirov's Chessbase DVD on the Phillidor.

This is a move I don't really understand all that much. I've seen it played in many variations of the queen's gambit declined and in the semi-slav but it never made much sense to me. In those positions Black usually captures on c4 or does something else but what if Black just allows White to play g4-g5? In a lot of the games I see the attack doesn't seem to go anywhere and if it does, it's due to what seems to be extreme circumstances, at least to me. 

I looked at an idea in the Jobava-Prie attack in which White played the move g4 very early in the opening. I'm not really interested in the theory but the idea behind this move. The engine I'm using says it's ok to play this but I really don't know why. I just let the engine play moves quickly just to see what it was thinking and that didn't really help. I know engines aren't the best in the opening but I was really at a loss as to what it was actually trying to do. And with very few games in this position, I couldn't really figure out what White wanted. Here's some of the moves:



What I also found odd was that one line gave 11.Qd2 Qa5 12.O-O which makes even less sense to me.