Position from my game. Why is b4 the best move here?

My engine suggests b4 here. I played through the moves and I have trouble seeing why this is the best move.  It likes all other moves much less.  It stops Qa5, but I don't think it's that big of a threat.  

Your space advantage is on the queenside.

The majority of your pieces are either on, or looking at the queenside.

The opponents king is on the queenside.

You want to open lines of attack against the enemy king. 

Everything points to playing on the queenside.

Middlegame Planning:

1. Expand your position:
2. Gain more space.
3. Improve the position of your pieces.
4. Decide on what side of the board to play.
5. Queenside: a-c files.
6. Center: d-e files.
7. Kingside: f-h files.

            Compare, space, material, and weakness(es)

            Play where you have the advantage.

3. DO NOT HURRY. Regroup your pieces, and be patient.

In any position with opposite side castling, it's standard for both sides to pawn storm the enemy king.

Let’s take a look at when it makes sense to castle opposite sides and when it doesn't.

You should castle on the opposite side when at least one of the following factors is true:

1. When you are up in development and your opponent has already castled, you should consider castling in the opposite side. That way you will have a clear game plan and will also be able to capitalize on your development advantage.
2. When you have a damaged pawn structure (doubled paws, missing pawns, far advanced pawns, etc.) on one of the sides you should consider castling on the other side.
3. When opponent’s pieces are especially active on one side of the board, it is usually best to castle on the opposite side.
4. If you want to complicate the game you may consider this option. That may be true if you must play for a win due to a tournament situation, when the draw is not enough. Also that maybe done when you're playing against a stronger opponent, who is much better in simple/technical positions. That maybe your best bet.

You should not castle on the opposite sides when at least one of the following factors in true:

1. When you are behind in development and you need extra time to develop your pieces, it is usually not a good idea to give your opponent a straight forward way of launching an attack.
2. When the opponent’s pawns are advanced towards the side you’re about to castle, it is not a good idea to castle there (especially if the opponent’s king is castled on the opposite side). It will just give him a positional edge in the attack.
3. When there are open/semi-open files in-front of the side you’re about to castle, you should probably reconsider your decision to castle there (especially if your opponent has castled on the other side). That will give him more attacking possibilities, such as rook lifts, various sacrifices, doubling of pieces on the file, etc.
4. If you playing against a weaker opponent you may want to avoid castling opposite sides, in order to avoid sharp game and keep everything under control.

Note: These are general rules, not laws, meaning that there are always exceptions to them. When you’re making a decision what side to castle you should always take your time and evaluate all “pros” and “cons” and base your decision upon your own analysis. This is a very important decision. It pretty much dictates which way the game will continue. Take your time and think twice.

Since it is opposite side castling the goal is to break open lines, b4 is a way you can do it to prepare b5 and b5 along with the a4-a5 so you can attack the queenside, and like said by @IMBacon a good amount of your pieces are on the queenside and also the center of the board so this means that breaking open lines and making imbalanes would be very good so you can reach to the enemy king first. 

It seems beneficial for you because your opponent doesn't have any pawns on the kingside and your king is well protected, while though the opponents king is protected you have pawns to attack it and make imbalances and weakening moves once you threaten to open up the position. 

Moreover it would seem to be ideal to have your rooks on the c, b or a file to look to threaten the king in a more direct manner, making them to be on their most effecient squares and threatin all types of tactics later on in which the position may be open after the pawn storm. Although even so it is absolutley fine that your rooks are controlling the center for the d and e files so honestly it is just a move of preference to line up with the king with the rooks. Regardless it seems like your opponent in this analyzed position has a lot to worry about unless they can get attacked in the next 5-7 moves and look to be in a precarious situation, and though you are not out of the clear yet, both sides looks like they have chances for active play in this middlegame and it will come to who can get to the king first in terms of activity, threats, checks and tactics as this is an attacking game.

Hopefully this was helpful @H1ghT1d3

you have space advantage on the queenside, black is castled queenside. 

very logical, the b4 push

@SNUDOO I think he was asking why it is such a logical move... lol that is why we are helping him, not to say it is logical move.

it's a logical move because black's king is on the queenside. Push pawns at their king, mate and win. 

easy

Yeah it is easy for us, but probably not for him... 

So this is why we are helping our fellow member.

I didn't know that pawn pushing was a viable strategy until I became over 1500 

it's really the only move, b4 I mean, besides pushing d5.

after Re3 black plays Ng4 

Opposite side castling = you should pawn storm the enemy king.

precisely

There is no principled way to go about the position, you can either pawn strom or steadily improve. Really it is up to the player, but also it is up to someone's styles and preferences as well.

Saying there is only a right way in chess is very funny, as that is the opposite objective of the game. Sure there are good moves and bad moves but it is also a game in which you have plenty of creativity so there is an abundance of moves that can be played if you think about it. Think about all those creative players such as Tal or Korchnoi if those players always played engine moves and not out of creativity they wouldn't be known as such brilliant attackers and middlegame executioners.

The only difference is the fact that the engines prefers b4, that doesn't neccessarily mean that b4 is the best or only move that can be played, as there are many options and chess and therefore many preferences as well by many different styles of players...

Re3 Ng4 is winning for black.

d4 doesn't lose a tempo after Bg4. First, take on c6, then take on e8, then play f3. Then take the d6 pawn (maybe)

Oh and Rb1 is too slow

for reference:

Re3 Ng4 double attack on h2 is winning. Nobody has to take on f2.

d5 Bg4 dxc6 bxc6 Rxe8 Rxe8 f3 Ne5 and then... let me see.