http://www.chess.com/games/view?id=12957#

Can anybody explain to me why the white resigned her? (in the last move)

36.Kb1 Re8 37.Rc2 Re1+ 38.Rc1 Re2

Sorry I'm like a very begginer 2 questions in this part why 37 Rc2

and what if the king moves to a1?

...Re8 threatens ...Re1+ (also if White plays Ka1). White plays Rc2 to answer ...Re1+ with Rc1 (impossible if White plays Ka1, that's why duck gave the more interesting Kb1 variation).

If 36. Ka1 it's mate in 8, if 37. Ka1 it's mate in 2.

Rc2 blocks mate after Re1 white goes Rc1.

After 36...Re8, Black threatens Re1#. 36.Kb1 and 37.Rc2 is the only way to prevent it (letting aside Queen/Rook sacrifices to delay checkmate).

Thanks for the explaination guys I get it now :)