Why is h5 a good move here?

Well, your absolutely dead lost if you can't pry black open and get at his king or use threats to win back serious material.  So its pretty obvious you can't worry about grabbing a pawn on the queenside.  More importantly, Rb8 and bb7 puts the bishop on a powerful diagonal your weak on, so spending a turn moving your queen to e4 doesn't make sense.  If white gets h5, where is the black knight going?  If be7 to make room on nf8, black's kingside is looking weak.  If black plays h5, then bd3 and the black kingside will get wrecked.   I haven't analyzed far enough to see any tactics, just saying, your dead lost if you can't create some weaknesses NOW.  Other than h4, what else is there to look at?  Ne5 looks like its a road to creating some accessible weaknesses, Stockfish confirms white has a viable attack, but I'd rather not trade off any more pieces.  Other than that, I dunno -- stockfish's bd5 and bd3 don't really appeal to me because black doesn't mind challenging that diagonal and trading off the bishops.  

Ok I understand most of what you're saying. How do you know its dead lost if no immediate weaknesses are created though? considering he has a rook, bishop and two pawns for the queen so material is roughly equal, plus his pieces are fairly bad placed? Thanks for responding.

Well maybe that was an overstatement, but you have weaknesses and an open king, he doesn't.  If you move your king back and forth a couple of times while he develops, Stockfish does in fact show you are losing bad.  Your advantage is this huge development lead.  You have to use it or lose it, because if black gets fully coordinated, the weaknesses in your camp might be telling.  Right now he is so poorly developed that he doesn't really have weaknesses, so you have to make some.  That is my thought process.  

I'm sure you've had similar situations against beginners that move their pieces back and forth and masters that do stupid stuff to taunt.  If you don't make weaknesses and/or otherwise exploit the activity, they get away with it.  Your winning . .  if you exploit your development lead to mess up his position so you can attack him.  

Not to mention that black has what would be a decisive material advantage if he wasn't so poorly developed on move 15

If you don't want string theorists to analyse, then don't utilise a 3D depiction!" - Pseudorandom person who has been eavesdropping on string theory conversations.

Another way to think about this is that a queen is only worth a rook, bishop and pawn if it can zoom around and attack multiple enemy targets.  Without weaknesses in the enemy camp, the queen is the inferior option.  So yeah, you aren't really down significant material, but it feels like that because black has no weaknesses at the moment.  Fortunately, you can use your huge development lead to make some.  H4/H5 both makes it harder for black to develop and creates weaknesses.  

True enough, but White's enormous advantage in development and mobility actually gives him a decisive advantage before 15.Qe4? 

No need to apologise, but we had better beware ourselves before a league of bosonic string theorists come along and start ranting on about the sublime properties of the number 26. Their most fruitful retaliation when faced with people detesting and reprimanding bosonic string theory is:

Z is the 26th letter of the alphabet. There exists no such thing as Z theory. On the other hand, our nefarious counterpart, string theory, cannot circumvent being some of the most generic entities roaming. The 11th letter of the alphabet is K. Algebraic K theory already exists. As such, string theory is not original and fails to possess the unique properties of bosonic string theory. Grothendieck has left the server.

I digress.

Addendum: I believe my comment may have sounded as a means of directing partial hatred of some sort. Sincerely sorry about that, I meant the pseudorandom person to not relate to you, but rather the crux of the letters themselves. The exclamation mark probably exacerbated the situation, so I apologise for this lack of congruity.

Go Harry!

First, I assume that you mean 15.h4 (not h5).

If so, the main reason is that a lot of master-level chess is restricting your opponent's pieces, or in this case, even driving them back. The Ng6 has no good squares, and h5 driving to to a worse square is threatened. If 15...Be7; 16.h5 Nf8, and not only has the Ng6 been driven back, and still has no good squares, but now the Rh8 is doing nothing, and white may get a direct attack against the Ke8, which is stuck in the middle. A specific line is 15.h4 Be7; 16.h5 Nf8; 17.Rg1 g6; 18.Ng5 with the threat of Qf3 hitting f7 and the Ra8. If Bg5 then the dark squares are critically weak.

That leaves only 15.h4 h5, but then 16.Rg1 Bb7; 17.Bd3 already has critical threats since black's king is not going to have anywhere safe to hide, and if the N retreats, we are back to similar ideas as above (Nf7 and the Rh8 problems).

As far as how you know when to do this, there is no hard-and-fast rule, but in this case, you have to realize that the pieces can be restricted, which is pure analytical work.

P.S. Let me also reference chapter 7 from the book "Find the Right Plan with Anatoly Karpov" (beware of this book in that the title in Russian is "Plan and Evaluation", and the book really is not really much about planning). The title of chapter 7 is: "The most important law of chess". That "law" is: "Restricting the mobility of your opponent’s pieces (and in association with this: domination by your own) – is the most important law of chess."

That is the primary thing that is going on with 15.h4. In conjunction with that is the weak K, and the fact that the Ke8, in essence, divides the board k-side and q-side, and prevents pieces f