Two pawns, two knights in the centre

It's hard to talk about when there are no moves for black shown (so many different things can happen)... in fact I've seen some coaches for beginners skip over this and give the student something more like this

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Or the mirror image (pawns on light squares with the light square bishop outside of the pawn chain).

I guess they do it because so many players put a pawn in the center that you'll never really get the setup your showed unless black is doing something like a pirc/KID.

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Having said that, to try and answer your question, it's better to think of all those pieces (the pawns, bishops, and knighits) as not in their final position yet. It's a nice setup because it's very flexible.

Let's imagine black's center pawns eventually do this (below)

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What does that mean? Well first of all if neither player touches their pawns, white has more room to maneuver. It's not a big advantage or anything but it's comfortable. If black captures, then white will have a pawn in one of the 4 center squares and black wont (again more room). If black doesn't capture, then white also has the option of putting a pawn or knight on d5.

No matter which center pawn moves, it will uncover a bishop, and the knights can go to either side (Nd2-g3 or Nd2-b3 are common enough maneuvers in various openings).

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I agree that it's a little cluttered... in particular I dislike blocking both my center files with minor pieces (I'll typically do something like put both bishops on the e file to keep my d file clear for a rook)... but like I said it's flexible and better to not think of these locations as final positions. You can only achieve this kind of setup when black is doing a solid but passive approach, so claiming space + flexibility is a reasonable way to go for an advantage.

I think what you are "missing" is something not really mentioned into more detail until about 1600-1800 rating. This is the concept of square weaknesses. For the time being, thinking in terms of piece development seems to be enough for most, but I like the question as this illustrates you trying to understand chess for yourself

What I mean by square weaknesses is the fact that whenever a pawn advances, it losses permanent influence over squares; this is because pawns can never retreat to guard squares they pass by. This is not the same for pieces (another reason to develop them early) because pieces can always retreat, relocate and improve themselves or cover squares they abandoned for the time being.

Let us imagine a new chess game starting and one side begins with 1. e4. "Innocent" pawn move (which is a good opening move, but this shows how ALL pawn moves have a certain drawback to them). Now this White e-pawn can NEVER influence the squares d4, d3, f4, f3 because the diagonal attacking of that pawn can't control these squares anymore. Pawns can't retreat once they advance forward. 

I don't want you to think 1. e4 is all bad (on the contrary, it does a lot of good things too). For instance, this e4 pawn now influences the squares d5 and f5. Every chess move leaves squares to gain squares, but pieces (Knights, Bishops, Rooks, Queen, King) can all move back if needed.

What happens if NO pawns can influence a square anymore? Let us say White moves 1. e4, 2. d4, 3. c4 (and we'll ignore Black's moves for now). Something inconsequential like 1. e4 e6 2. d4 Ne7 3. c4 Ng8. Well, now we have something called "holes." These are squares which are potentially weak because one side can no longer defend these squares with a pawn. In this position, d3 is one example of a "hole" in White's position.

In this example, White is surely better because they have more control of the center (although both sides have done nothing much for piece development or castling early in accordance to chess opening principles: 

https://www.chess.com/blog/KeSetoKaiba/opening-principles-again 

If d3 is a hole for White, then isn't this bad for White? From this standpoint, yes. Yes it is. However, EVERY chess move has pros and cons and some weaknesses like holes are less meaningful than others. Black really has no way to exploit this hole on d3. A hole (or weakness, target, positional flaw etc.) is really only significant if the opponent is able to make use of it.

I gave this made up position just to explain what a hole is by definition (a square which a pawn can no longer defend). 

There is less need to advance your c-pawn or f-pawn (Knights in the way on c3 and f3) because White may not want to advance pawns anyway. Clearly, not moving pawns at all can't be right, but the chess player must find a balance. The stronger players will think twice about a pawn move because it can't be un-done (pieces can admit the plan was wrong and retreat back, but pawns can't move backwards) and therefore, pawns advancing leaves holes in their position.

Why are holes potentially problematic? If the enemy pieces can land on your weak squares (holes), then a pawn move can't kick them away and the enemy pieces can become annoying to remove. If the enemy successfully gets a piece to a hole and has it supported by a friendly pawn, then this is called an "outpost" like move 12 in this position. See if you can find the best move for White

Yes this is it! The player with the White pieces noticed that the e6 square was a hole in Black's camp (a Black pawn can't ever influence e6 because the e7 pawn attacks diagonally at d6 and f6. White's e5 pawn supporting this piece makes the e6 Knight an outposted piece and really powerful, since it is tough for Black to ever remove.

By the way, the puzzle position I gave was from a game I played on chess.com and also wrote a chess article on this game elsewhere. The game was fairly advanced, but here is the article if you are interested. You don't have to grasp all the nuiances, but you can at least look for outposts and weak squares. Training your mind to see these things will indirectly help as you'll naturally notice them in your games too

https://www.chesshere.com/forums_topic.php?id=88000