Why is Nh4 such a good move in this position?

Hi and happy new year!

To start off, I'm a complete beginner. I started playing chess about a month ago after watching the Queen's Gambit and I'm trying to learn the basics.

So I was analyzing one of my games (I'm white) and the engine is telling me that I have two missed wins. In move 16 I'm loosing and he makes a triple threat against my h2 pawn, which I block with 17. g3 Kf7. For move 18, 19 and 20 the engine tells me that Nh4 is the best move and for 19 and 20 it could've even swung the game around in my favor (at least that's what missed win means, right?). But no matter how much I look at it, I just don't understand why Nh4 is such a good move. Could someone please explain it to me?

"I started playing chess about a month ago"

But you are using an engine already to analyze your games?

Nh4 is good because you get a free bishop and/or you are also caging in the king a bit.

Oh, I see it now! That would've been a nice advantage.

"But you are using an engine already to analyze your games?"

Maybe engine isn't the right word for it? I meant the chess.com analyze thing on the computer. How else do I find out what I did wrong? I thought the other guy was pretty good but apparently it was a mistake festiveal on both sides

Anyway, thanks for taking the time to reply!  

"Maybe engine isn't the right word for it?"

Technically, it is an engine. However, it produces limited results. 

If you look at the depth mentioned, in the upper right it defaults to depth 15. The higher the number the better off you are as far as looking for the best move. However, this takes some experience and understanding to properly make use of moves mentioned.

A lot of times, we won't understand what the engine is producing when it goes deep in analysis. The Nh4 move is more basic and easier to understand. But let's look at earlier in the game. It suggests 3...f6 for black.

As a general rule, f6 is not a good move to make. It is better to play Nc6. So, you have to click on the gear icon and you will see d6 and Nc6 also mentioned. This was using their Stockfish 11 engine.

I have Stockfish 12 and it is showing Nc6 is the best move at depth 31. Nc6 is also a good idea to get used to playing first. In some games, d5 is also played. So, d6 could be considered a loss in tempo if you want the pawn on d5 later. It all depends on position, but if you are a beginner, what I am trying to get at is you have to decide to go with Nc6, which I would start with before experimenting with d6, or play d6. The f6 result after depth 15 is too contextual in my opinion. It doesn't come up as often.

Interesting to get a better understanding of how the engine works. I get what you're saying about the different moves, although I would never have seen this myself, at least at this point in time .

nh4 gets an easy knight after 19. nh4+ kg7 20. bxg4. also, after moving to h4, you could also consider moving to f5 which is a good square for your knight.

Your question is a good one. Don't just accept engine recommendations without trying to understand them. In the case of Nh4+, the answer is tactics! You have a potentially lethal attack on the black king, If you keep playing, you will start to recognize these situations more quickly and more often. Here are a few variations to show what might happen after 19.Nh4+