Think of a data structure as a tree. A shallow clone clones the root of the tree and shares the subtrees of the original tree's root. A deep clone is a recursive copy, i.e. all data structure components in the clone are copies of those in the original. In this case every non-leaf node in the tree would be a copy of the corresponding node in the original. Thus the name shallow vs deep.
Btw this terminology comes from LISP where you could do shallow and deep copies of lists. In this case the shallow copy copied only the top-level of the original list and the deep copy all levels of same.
Note that this topic has been discussed a few times around these parts before. If you're interested in reading a few more explanations, I'd suggest trying a quick search on this and the intermediate forums. (The search page link is at the top right of this page.)