An explicit instantiation definition creates and declares a concrete class, function, or variable from a template, without using it just yet. An explicit instantiation can be referenced from other translation units. This can be used to avoid defining a template in a header file, if it will only be instantiated with a finite set of arguments. For example:

// print_string.h
template <class T>
void print_string(const T* str);

// print_string.cpp
#include "print_string.h"
template void print_string(const char*);
template void print_string(const wchar_t*);

Because print_string<char> and print_string<wchar_t> are explicitly instantiated in print_string.cpp, the linker will be able to find them even though the print_string template is not defined in the header. If these explicit instantiation declarations were not present, a linker error would likely occur. See http://stackoverflow.com/questions/495021/why-can-templates-only-be-implemented-in-the-header-file

If an explicit instantiation definition is preceded by the extern keyword, it becomes an explicit instantiation declaration instead. The presence of an explicit instantiation declaration for a given specialization prevents the implicit instantiation of the given specialization within the current translation unit. Instead, a reference to that specialization that would otherwise cause an implicit instantiation can refer to an explicit instantiation definition in the same or another TU.

foo.h

#ifndef FOO_H
#define FOO_H
template <class T> void foo(T x) {
    // complicated implementation
}
#endif

foo.cpp

#include "foo.h"
// explicit instantiation definitions for common cases
template void foo(int);
template void foo(double);

main.cpp

#include "foo.h"
// we already know foo.cpp has explicit instantiation definitions for these
extern template void foo(double);
int main() {
    foo(42);   // instantiates foo<int> here;
               // wasteful since foo.cpp provides an explicit instantiation already!
    foo(3.14); // does not instantiate foo<double> here;
               // uses instantiation of foo<double> in foo.cpp instead
}