In shell-speak, globbing is what the shell does when you use a wildcard in a command (e.g. * or ?). Globbing is matching the wildcard pattern and returning the file and directory names that match and then replacing the wildcard pattern in the command with the matched items. Bash version 4.0 adds a new globbing option called globstar which treats the pattern ** differently when it's set.

Normally, if you use the pattern ** on the command line it acts the same as the * pattern. For example, given the following directory:

$ ls -l
total 8
-rw-r--r-- 1 mitch users    0 2010-05-05 10:36 a
-rw-r--r-- 1 mitch users    0 2010-05-05 10:36 b
drwxr-xr-x 2 mitch users 4096 2010-05-05 10:36 c
drwxr-xr-x 2 mitch users 4096 2010-05-05 10:36 d

if you execute the following commands:

$ for i in **
> do
>   echo $i
> done

you get the following output:

a
b
c
d

If you now set the globstar option with the following command:

$ shopt -s globstar

and then re-run the for loop from above, you now get:

a
b
c
c/e
d
d/f

With globstar set, bash recurses all the directories. Note that this will recurse all directory levels, not just one level.

You can see if globstar is set by issuing the shopt command without any arguments:

$ shopt
...
force_fignore   on
globstar        on
gnu_errfmt      off
...

or if you want to test it in a script you can use the -q option to shopt and test the exit status, for example:

if shopt -q globstar; then
        ...
if