The non-greedy modifier simply means "match as little as possible while still getting a successful match". All regex matches in Perl Compatible Regular Expressions always match leftmost first; in your case the first slash. Where the non-greedy operator might have worked, for example, is if you wanted to only match 'foo'. Then you could write:

This will match the first slash, then non-greedily match any other characters until another slash is reached. If you didn't use the non-greedy modifier here, you would match everything between the first and last slash (i.e. 'foo/bar/baz').