Do not delete /private!
The stuff in there is part of the OS and required. Normally Apple normally keeps it (finder) hidden from "prying eyes" 😉 I don't know how it became finder visible for you.
FWIW, if you have the Developer Tools installed you can execute the following commands from the Terminal to make it hidden again:
sudo setfile -a V /private
killall Finder
The second command is just to relaunch the finder at which point /private should be hidden.
If you don't have the Developer Tools installed, don't let it bother you. It's just one of many other (hidden) directories in the root directory. It doesn't matter whether its invisible or not. Only that what's in there stay there!
Also, I believe there a a few third party apps to selectively hide/unhide files. I just don't recall any specific one at the moment.