The main issue:
You're passing a std::string to printf, and trying to display it with a %s. printf is a C function (not C++), so it expects to receive strings of type "char*", not "std::string".

The correct way to pass a C++ string to C's printf is:

printf("item Name: %s\n", myHero.storage[i].c_str());

or in C++:

cout << "item name: " << myHero.storage[i] << endl;

Other issues:
You have using namespace std; in a header file. This should only ever go in cpp files, not h files.

(You can google "using namespace in headers" to find discussion on that point, e.g. http://stackoverflow.com/questions/5849457/using-namespace-in-c-headers)

addStorageItem is passing std::strings by value. This creates extra temporary copies of them. You should be passing them by const-reference:
void Hero::addStorageItem(const string& x):

Hero has an empty constructor and destructor. If they don't do anything, you can just not write them.
In your header file, Hero doesn't have a constructor or destructor -- so the fact that you have them in your cpp file means this code shouldn't compile at the moment ;P

Hero myHero = Hero(); is redundant. This code says to construct a temporary unnamed Hero object, then to copy construct myHero using that temporary.
You can just write: Hero myHero;