Let me explain this in a little more detail. Consider the folowing
class foobar
float * fpoint;

Now in the copy constructor I might just copy the value of fpoint into the new class(which is called a shallow copy) . This means that fpointnew and fpoint point to the same memory location and if I try and alter this memory location using fpointnew I end up also changing the value fpoint(old) points to. In a deep copy a copy constructor would be used to create a new location for the new pointer to point to, thus avoiding this problem.