Implementing Conway's Game of Life
#includes should not end with a semicolon:


#include "gameOfLife.h";



The reason this is incorrect is because this is a preprocessor directive, which do not follow the same syntax as compiled lines.
Instead of using a typedef:


typedef std::vector&lt; std::vector&lt;int&gt;&gt; gridVector;



you can now use C++11's type alias:

using std::vector&lt;std::vector&lt;int&gt;&gt; = gridVector;

If you don't need the default constructor, you can either leave it out or make it explicitly defaulted:

gameOfLife() = default;

There's really no need for multiple public and private sections.  If you prefer to organize or separate the members in some way, you can just add line breaks.
I'm not sure why you have a *gridCopy member.  Not only would it be more natural to use a copy constructor in such cases, but having a raw pointer as a member would "force" you to have an overloaded copy constructor.  This is because the default copy constructor performs shallow copies, which will copy the pointer instead of the value at that pointer.

After removing this member, you should also remove copyGrid().
I'm not too familiar with GoL, but I don't think that while loop in run() is supposed to run infinitely.  This type of while loop will not stop unless a break or return is encountered.  You may need to modify it in such a way that it can end.