Creating a subverson repository not possible because button is grayed out?

as you can see in the image I attached here:

http://im开发者_开发问答g202.imageshack.us/img202/6497/subversion.png

the button to browse the DIR to set the repository directory is grayed out, but why?

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It is clear because you have never entered a repository before. That button is for navigating within a repository that is in the text box to the left of that button. Type it in manually. Then it will remember it in future checkouts and you can then press that button to navigate it.

If your intent is to create a repository, you are selecting the wrong function. Select "create repository here" in the TortoiseSVN context menu.