Is there any strategic importance in having pawns at the centre of the board? Please provide a detailed explanation.
I'm going to assume that the importance of the center in general terms is already something you are aware of. In short, controlling the center means that your pieces will be able to access/utilize the whole board much better than if your opponent does.
Pawns allow a strong control of the center by virtue of the fact that they are both weak (meaning your opponent will be unlikely to trade a stronger piece for one) and the fact that they cannot move backwards or readily across files (meaning that it's relatively easy to create situations where one side's pawns cannot be attacked by the opponent's pawns, even if material is even). This of course assumes that one player is occupying the center with pawns (see: 'big center') and the other is not.
A more likely situation is one where both players are occupying the center with pawns, and the more important effect of this is that it helps determine the character of the game. If the center is blocked, the position is often vastly different to when the center pawns are traded for each other, leaving plenty of room for the long-range pieces to move around. Neither of these situations is inherently better for one side, but can allow a player to reach positions they are more comfortable with, or use their pieces more effectively than the opponents (e.g. a wide-open position can generally be said to favor a side that has bishops instead of knights, if there in an inequality there).
Is it important to have pawns at the centre of the board?
No it is not. Actually, it is not mandatory. To understand why, we must go down the chess history lane a bit.
In the old days, there was an opinion that if you don't have pawns in the center you can't really count to survive the game.
Practice showed the wonderful benefits of pawn center: they can move forward, pushing away opposing pieces into passive or simply bad squares, while weakening opposing pawn structure. The further they advance, the greater the chance for their owner to get extra piece, since there is no other way to stop their promotion. If you manage to somehow block them, you are still in danger -> you need time to organize your badly placed pieces and your good pieces are restricted in action because they have to block the central pawns. Furthermore, you will find yourself lacking space for maneuvering. Meanwhile, owner of the central pawns gains HUGE amount of time and strong central outposts for his pieces, not to mention space advantage.
It is no wonder why such games ended fast in favor of the side owning central pawns. One good illustrative example is the following one:
[Title "Italian game"]
1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.c3 Nf6 5.d4 exd4 6.cxd4 Bb6? 7.d5 Ne7 ( 7...Na5 8.Bd3 c5 9.d6! ) 8.e5 Ng4 ( 8...Ne4 9.d6 Nxf2 10.Qb3 ( 10.Qe2 Nxh1 11.Bg5 Bf2+ 12.Kf1 c6 13.Bxe7 Qb6 14.Ng5 Rf8 15.Qh5+- ) 10...Nxh1 11.Bxf7+ Kf8 12.Bg5! ) 9.d6 cxd6 ( 9...Bxf2+ 10.Ke2 ) 10.exd6 Nc6 11.Bg5!
Things got even worse when Queen's Gambit was discovered. Since White was able to always return the gambited pawn and maintain central dominance all GMs of that time switched to
1.d4 since all Black could do is to fight for a draw from the very start. He could never create really dangerous counterplay. The game started dying, which is best illustrated in Capablanca-Alekhine world championship match.
Soon a rebellion came in view of young masters who were prepared to take radical measures in order to revive the game, and improve Black's chances to win. They came to an idea to control center from afar with pieces only but that didn't turn out well. Their movement was called hypermodernism. In the end, space advantage provided by central pawns was too much to offer equality. Although it was enough in the beginning, over time White would simply "suffocate" Black. Hypermodernists recognized that they need to include pawns as well into the fight and once that happened chess was saved. A whole new set of openings was created and they were playable.
The dogma of having pawns in the center in order not to lose was crushed and new strategy was born. An opening that best illustrates this principle is the main line of the Grunfeld's defense. Here is an illustrative game that shows hypermodern concept of battling pawn center with pieces:
[White "Alexander Alekhine"]
[Black "Ernst Gruenfeld"]
1. d4 Nf6 2. c4 g6 3. Nc3 d5 4. Bg5 Ne4 5. cxd5 Nxc3 6. bxc3 Qxd5 7. Nf3 Bg7 8. e3 c5 9. Bb5+ Bd7 10. c4 Qe4 11. O-O Bxb5 12. cxb5 Nd7 13. Rc1 b6 14. Qb3 h6 15. Bh4 O-O 16. Rc4 Qe6 17. Rd1 Rfe8 18. d5 Qd6 19. Bg3 e5 20. dxe6 Qxe6 21. Rd6 Qe7 22. Ra4 Nf8 23. Qd5 Rad8 24. Nd2 Rxd6 25. Bxd6 Rd8 26. Nc4 Qd7 27. h3 Ne6 28. Qe4 Bf8 29. Bxf8 Qd1+ 30. Kh2 Qxa4 31. Be7 Re8 32. Bf6 Ng7 33. Qd3 Qxa2 34. Bb2 Re6 35. Qc3 f6 36. Qd3 h5 37. e4 Qa4 38. Nd6 Qb4 39. Nc4 Qxb5 40. f4 Qc6 41. e5 f5 42. Nd6 Re7 43. Qg3 Kh7 44. Qg5 Qd7 45. Qg3 Ne6 46. Qf3 b5 47. Qa8 Qd8 48. Qd5 b4 49. g3 a5 50. Qc6 Qd7 51. Qa6 a4 52. Ba1 a3 53. Qc4 Qc6 54. Kg1 Qf3 55. Kh2 Qf2+ 0-1
This prelude is important for your next question:
Is there any strategic importance in having pawns at the centre of the board?
Yes. To continue from above: although Black was able to "snipe" White from afar, and counterstrike his center from wings, White found a way to fight for advantage, thanks to his central pawns.
Nowadays, White will use central pawns to seize space thus containing Black's development advantage. He also is the one who usually has more plans available as he has stronger presence in the center. This is best illustrated in King's Indian defense -> Black usually has only one good plan, to push
...f5, while White's space advantage ( which stems from his central pawns ) gives him several plans available: he can open center, he can castle kingside launching queenside action, he can castle queenside launcing kingside pawnstorm, and he can try to control entire board by leaving king in the center and play
g4 ( I think this is called Makagonov system ).
King's Indian defense and Grunfeld defense really illustrate well pawns in center vs no central pawns pros and cons.
I am too tired to continue, and I slowly start to lose my focus so I will top here. If you have further questions leave a comment. Best regards.