CAN anybody explain me this puzzle.

I will explain puzzle #171 step-by-step.

First of all, let us focus on what is given to us in the puzzle.
a) Material
White: 8 draughtsmen (checkers); black: 8 draughtsmen (checkers).
Material is equal, therefore, white should gain material advantage or get strong king for winning.
b) Positional evaluation
White has more freedom for acting in this position; black is very cramped. Probably, the best idea for achieving a draw for black would be to make an exchange 18-22 27x17 23x12 and afterwards to launch attack against white left flank.
c) Positional weaknesses
White has no weaknesses (even edge draughtsman 26 is good, because it blocks and delays breakthrough). Black has holes on squares 11 and 12; besides, black has a bunch of juicy draughtsmen on 7, 8, 9, 17, 18, 19 which gives an impression that white should try to find a shot.
d) White tactical resources
White has nice column 29-34-40. In similar positions white could try to apply majority capturing idea 26-21 if white manages to create in-between move (sometimes called "free tempo").
White should to try to explode black camp with sacrifices 26-21 and 27-22.
And, indeed, after

1. 26-21 17x21 2. 27-22 18x27 3. 29x18 13x22

white delivers winning shot

4. 37-32 27x29 5. 34x1

and white is winning.

Just only for beginners: the best chance for black would be 5. .. 22-28, but after 6. 1-18 white king restricts black draughtsmen 16 and 26. Black can't advance 6. .. 28-33 due to 7. 18-22, but, if 6. .. 28-32 the simplest winning (but maybe not the quickest) technique for white would be 7. 30-25 (waiting move; white wants to attack 18-27 or 18-23) 16-21 8. 18-27 32-37 9. 27x16 26-31 10. 16-38. White provokes black to play 10. .. 37-42 for trapping the new born black king: 11. 38-32 42-48 12. 40-34, but if black attempts to show resistance with 10. .. 31-36, the best idea, of course, is to sacrifice white king: 11. 38-42 37x48 12. 40-34, and black should surrender.