Cloning is for the sheep. Cloning a sheep called Dolly makes another identical sheep called Dolly2. However, suppose that Dolly has a baby lamb. If we shallow clone Dolly, then Dolly2 will think that the lamb is hers too, and Dolly will not like that at all.
But if we deep clone Dolly, then we have to clone the lamb too. Then for Dolly2 all is fine because she has her own baby lamb to care for.