By default, the search string is matched exactly (but without regard to case, unless pickaxe is selected). However, when you check the re checkbox, the pattern is interpreted as a POSIX extended regular expression (also case insensitive).

Search options

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 a git-grep peculiarity, currently if regex mode is turned off, the matches are case-sensitive.
author
Name and email of the author and date of the patch will be scanned for the given pattern.
committer
Name and email of the committer and date of commit will be scanned for the given pattern.
pickaxe
All commits that caused the string to appear or disappear from any file (changes that added, removed or "modified" the string) will be listed. This search can take a while and takes a lot of strain on the server, so please use it wisely. Note that since you may be interested even in changes just changing the case as well, this search is case sensitive.