Conceptually, what makes the Sicilian opening sensible for black? We all know the Sicilian as shown below, is one of the most famous and commonly employed openings in chess. But compared to the other replies, which tend to be more about fixing the center (such as e5, or the French e6-d5, Caro-kann c6-d5), the Sicilian tends not only to not fix the center, at least more often than not,
but it also starts from a pawn non-central pawn move which doesn't liberate any of our bishops or knights. On top of that, it is not a move on our kingside, which means relative
to white's e4 we will be slower in developing our kingside pieces. As opposed to starting with e5 and still stopping d4.

I started pondering this question after I had read the discussions on this post, which was about the point behind Ruy-Lopez and why it's good for white.
So considering those discussions and the above points, my question is:


At a conceptual and strategic level, what makes the Sicilian a sensible opening for black?


Diagram:

 [title "The Sicilian opening"]
 [fen "rnbqkbnr/pp1ppppp/8/2p5/4P3/8/PPPP1PPP/RNBQKBNR b KQkq - 0 2"]
Note: Discussions are primarily from black's perspective.

It may be relevant to remind that one way or the other, most often, the Sicilian continues with white preparing the d4 pawn push, which leads to a trade of the c5-d4 pawns.
Common starting lines are shown in the following diagram:

 [title "common starting lines"]
 [fen ""]

 1.e4 c5 2.Nf3 Nc6 (2...d6 3.d4 cxd4 4.Nxd4 Nf6) (2...e6 3.d4 cxd4 4.Nxd4 Nf6 5.Nc3 Bb4) (2...g6 3.d4 cxd4 4.Nxd4 Bg7 5.Nc3 Nc6 6.Be3 Nf6) 3.d4 cxd4 4.Nxd4


At a very basic and fundamental level, the Sicilian 1.e4 c5 achieves the following:


Claims immediate control over the center, otherwise white would happily take the full sweet center with e4-d4.
Leads to a trade of a non-central pawn (c7) for a white's central pawn (d2)!
Provides a certain degree of flexibility in how to commit the central e-d pawns. And also breaks the symmetry right from the start, which tends to make the continuation of the game more dynamic.


For the purposes of your question, I will further expand on the first two points:

Expanding on point 1:

Claiming their share of control over the center: white's e4 actives the queen and bishop, but more importantly it provides light square control in the center as it takes away d5-f5 from black. That does not mean d5 is unplayable, in fact that opening exists (see Scandinavian Defense) but it simply means black can't establish a pawn on d5 and maintain it, as white will immediately take. Similarly, black's c5 in return, provides dark square control as it controls b4 and more importantly d4. On the plus side, it stops white from landing a pawn on d4 without having had to commit their central pawns (black's e &amp; d pawns remain flexible still). But on the other hand, c5 is not a move that provides activity to any minor piece, in fact it only activates the queen, therefore, the setback of it is that it doesn't directly contribute to black's minor piece development, as you also hinted at in your question.

And on point 2: not all pawns are equal

At a basic level of pawn consideration: the Sicilian almost always leads white to trade a central pawn for a non-central pawn, and that in itself is a gain for black!

To see why consider the following thought process: generally, we say pawns have a value of 1, as a means of quantifying their worth relative to the other pieces, which are dynamically faster and move reversibly. But amongst the pawns themselves, do they all have the same value still? 

Well let's consider e.g. white's queenside pawns: the a2 pawn which is at the boundary of the board, only provides control over one square, namely b3. In contrast, the b2 pawn being slightly away from the boundary, provides control over 2 squares, a3 and c3. And even when you push these pawns, the relative control they provide remains similar. However, things become more interesting towards the more central pawns: the c2 pawn, also provides control over 2 squares, but when pushed for example to c4, it also provides us with control over a central square, namely d5, and a non-central and less important square, b5.  

And finally, the pawn on d2, when pushed to d4, it provides control over a central (e5) square and a near-central (c5) square, meaning it secures more central space than a c pawn is capable of doing2. So, with all that in mind, doesn't it stand to reason that the central pawns are in fact worth more than the side pawns? and indeed it does. Intuitively, if you imagine the b2 pawn being worth 1, then the a2 pawn is something like 0.9, and the d and e pawns are probably close to 1.1-1.2. But the absolute values you assign to them do not matter much, it's more important to remember conceptually their differences.
To conclude this point, in the Sicilian, black is in fact exchanging the pawn on c7 for the pawn on d2, so clearly, black's getting away with a better deal in that regard1.

I guess the common denominator of all these discussions and different points boils down to the control over the center. This cannot be emphasized enough: Having the center, your pieces move and reroute more efficiently across the board, they also see a larger portion of the board when centralised. So much like the pawn comparison above, it's as if their relative worth increases when they are placed more centrally. Compare a bishop on e5 which sees 13 other squares distributed over two diagonals (so sees both the king and queen side), to a bishop on h8 which sees 7 squares only, and all of them along the same diagonal. 



Two Caveats:

1: All things considered, it begs to ask: doesn't all this mean that black should even be better by playing the Sicilian? What does white have to gain by allowing all this?
Short answer: tempo and initiative. 
Longer answer: To understand these things you need to always remember than chess is never that linear, and that there are many more angles to consider before we can fully assess a position. In this case, white has the better activity and develops more efficiently. These stem from the fact that in the Sicilian white's first 2 pawn moves in the game are (often) e4 (by definition) and d4 (after being prepared by Nf3). Thus, both our bishops are activated, and nothing prohibits our knights from being developed centrally. Sure, white trades a better d2 pawn for a c pawn, but in return the d file becomes semi-open for white, along which white will exert pressure (and so should do black along its own semi-open file, namely the c file). Being up in development means we castle faster, and have more pieces in play, so white will still be for the most part dictating the flow of the game.  

2 One might ask whether the relative worth of the e-f-g-h pawns follows symmetrically from the discussion of the queenside pawns.  Partly yes, but major difference is that these are kingside pawns, and as such, their movement leaves behind weaknesses around the king. So if you will, the king is what breaks the symmetry between the left and right side of the board. For example, when the c2 pawn moves, it leaves light square weaknesses behind it but these are squares that are of lesser concern for black as often the king will not lie behind them. In contrast, when the f pawn moves, it weakens the dark squares around the king and exposes it to diagonal attacks (and leaves holes for pieces to land on near your king.)