Pattern is by default a normal string that is matched precisely (but without regard to case, except in the case of pickaxe). However, when you check the re checkbox, the pattern entered is recognized as the POSIX extended regular expression (also case insensitive).

commit
The commit messages and authorship information will be scanned for the given pattern.
grep
All files in the currently selected tree (HEAD unless you are explicitly browsing a different one) are searched for the given pattern. On large trees, this search can take a while and put some strain on the server, so please use it with some consideration. Note that due to git-grep peculiarity, currently if regexp mode is turned off, the matches are case-sensitive.
author
Name and e-mail of the change author and date of birth of the patch will be scanned for the given pattern.
committer
Name and e-mail of the committer and date of commit will be scanned for the given pattern.