Please show an example of the triple repitation checkmate

I think you mean 'threefold repetition', which is a draw.

Thank you very very much!

Isn't it a draw already after 4...Kg8 ?

Since before a move was made there was already a position

Lets say black's move before the initial position ( sort of a premove ) is

0...Rf8 ( only possible last move for black )

So After

0...Rf8

2...Kg8

4...Kg8

A position already appeared thrice so couldn't you already claim the draw after 4...Kg8?

It's the three fold repetition rule, and it's not a checkmate.

Sorry, I was in hurry and instead of writing draw I wrote checkmate

Guys my question above seriously....

Yes indeed; I missed that.

So, can the draw be claimed even after moves have been made that break the repetition (e.g. the capture of pieces)? So, if white massively messed up and lost all but his king and black still has this rook (and maybe even his pawn to promote), he could claim the draw even though black can force checkmate? I'm unsure of this.

No, according to FIDE rules you must claim a draw while position which is currently on the board(or will be after your move) is repeated at least 3 times including possible moves - castling and en passante