Using ** instead of * means that you want to have recursive globbing from that directory level on.
For example
Code:
tobi ~/test ☺ $ tree
.
├── a
├── b
│** ├── c
│** │** └── d
│** │** └── y.txt
│** └── y.txt
├── c
│** └── y.txt
├── d
└── e
7 directories, 3 files
tobi ~/test ☺ $ echo */y.txt
b/y.txt c/y.txt
tobi ~/test ☺ $ echo **/y.txt
b/c/d/y.txt b/y.txt c/y.txt
As you can see, the ** version will find all files y.txt in the tree, the version with the single asterisk will work the usual way.
This makes it easier to launch commands on files in unknown places without having to use the find command, but it is limited by the maximum length of the commandline your shell allows (which is usually pretty high).