The key idea behind implicit sharing seems to go around using the more common term copy-on-write. The idea behind copy-on-write is to have each object serve as a wrapper around a pointer to the actual implementation. Each implementation object keeps track of the number of pointers into it. Whenever an operation is performed on the wrapper object, it's just forwarded to the implementation object, which does the actual work.
The advantage of this approach is that copying and destruction of these objects are cheap. To make a copy of the object, we just make a new instance of a wrapper, set its pointer to point at the implementation object, and then increment the count of the number of pointers to the object (this is sometimes called the reference count, by the way). Destruction is similar - we drop the reference count by one, then see if anyone else is pointing at the implementation. If not, we free its resources. Otherwise, we do nothing and just assume someone else will do the cleanup later.
The challenge in this approach is that it means that multiple different objects will all be pointing at the same implementation. This means that if someone ends up making a change to the implementation, every object referencing that implementation will see the changes - a very serious problem. To fix this, every time an operation is performed that might potentially change the implementation, the operation checks to see if any other objects also reference the implementation by seeing if the reference count is identically 1. If no other objects reference the object, then the operation can just go ahead - there's no possibility of the changes propagating. If there is at least one other object referencing the data, then the wrapper first makes a deep-copy of the implementation for itself and changes its pointer to point to the new object. Now we know there can't be any sharing, and the changes can be made without a hassle.
If you'd like to see some examples of this in action, take a look at lecture examples 15.0 and 16.0 from Stanford's introductory C++ programming course. It shows how to design an object to hold a list of words using this technique.
Hope this helps!
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