Shallow copies duplicate as little as possible. A shallow copy of a collection is a copy of the collection structure, not the elements. With a shallow copy, two collections now share the individual elements.
Deep copies duplicate everything. A deep copy of a collection is two collections with all of the elements in the original collection duplicated.
In short, it depends on what points to what. In a shallow copy, object B points to object A's location in memory. In deep copy, all things in object A's memory location get copied to object B's memory location.
The Wikipedia article Object copy has a great diagram.
char * Source = "Hello, world.";
char * ShallowCopy = Source;
char * DeepCopy = new char(strlen(Source)+1);
strcpy(DeepCopy,Source);
'ShallowCopy' points to the same location in memory as 'Source' does. 'DeepCopy' points to a different location in memory, but the contents are the same.
'ShallowCopy' points to the same location in memory as 'Source' does. 'DeepCopy' points to a different location in memory, but the contents are the same.