Originally Posted by allwimb
Booting on single user mode give you more rights so that you can troubleshoot the system.
this is not true! In fact in most cases root will be logged in in single user mode and root has always all permissions.
Single user mode means that only one user (in most cases root) will log in. The system runs with only a few services in order to access the filesystems.
One can start additional services also in single user mode. So you will be able to get even a network-connection in single user mode.
If you want to know more, you should read about runlevels. Runlevels differ only in the services they have available. http://en.wikipedia.org/wiki/Runlevel
Note that the definitions of the various runlevels differ between the distributions.