I've always had this doubt. Since I'm not so good a chess I couldn't imagine the idea behind this game. Can someone please help me out?

The following position is a typical Benoni Defense.

I didn't get why black pawn has to be pushed to c5, while it can be taken by the white pawn at d4? Tell me if there are any shortcomings if the white takes the black pawn.

Dxc5 is probably not the best to play. Black can respond with e6 (attacking the pawn) and from there white should give black the pawn back. If he plays Be3 then black can play Na6 and white cannot further defend his pawn while the bishops hinders the movement of the e pawn.

Yes, when the Benoni is seen these days at all, it is usually from the Modern Benoni move order 1. d4 Nf6 2. c4 c5 3. d5, when Black can choose the classical ...e6 or delay this with ...g6, ...Bg7, ...0-0 etc first, or try the Benko Gambit with ...b5!?

The move order 1 d4 c5 is bad, because White can play 2 d5 and is under no obligation to play c2-c4, using that tempo for development instead and Black can come under serious pressure early.  For example 2 ...Nf6  3 Nc3 d6  4 e4.  This is also the problem with the "Franco-Sicilian" move order after 1 e4 e6  2 d4 c5?!  3 d5 exd5  4 exd5 Nf6  5 Nc3 d6  6 Nf3. 

Thanks for all that info guys!