Caveat: It is not necessary to put the implementation in the header file, see the alternative solution at the end of this answer.

Anyway, the reason your code is failing is that, when instantiating a template, the compiler creates a new class with the given template argument. For example:

template<typename T>
struct Foo
{
    T bar;
    void doSomething(T param) {/* do stuff using T */}
};

// somewhere in a .cpp
Foo<int> f; 

When reading this line, the compiler will create a new class (let's call it FooInt), which is equivalent to the following:

struct FooInt
{
    int bar;
    void doSomething(int param) {/* do stuff using int */}
}

Consequently, the compiler needs to have access to the implementation of the methods, to instantiate them with the template argument (in this case int). If these implementations were not in the header, they wouldn't be accessible, and therefore the compiler wouldn't be able to instantiate the template.

A common solution to this is to write the template declaration in a header file, then implement the class in an implementation file (for example .tpp), and include this implementation file at the end of the header.

Foo.h

template <typename T>
struct Foo
{
    void doSomething(T param);
};

#include "Foo.tpp"

Foo.tpp

template <typename T>
void Foo<T>::doSomething(T param)
{
    //implementation
}

This way, implementation is still separated from declaration, but is accessible to the compiler.

Alternative solution

Another solution is to keep the implementation separated, and explicitly instantiate all the template instances you'll need:

Foo.h

// no implementation
template <typename T> struct Foo { ... };

Foo.cpp

// implementation of Foo's methods

// explicit instantiations
template class Foo<int>;
template class Foo<float>;
// You will only be able to use Foo with int or float

If my explanation isn't clear enough, you can have a look at the C++ Super-FAQ on this subject.

What are precompiled headers?

Often C++ source files include headers from external libraries. In Windows you include windows.h. These header files can be very large and they take some time to process. Each time you compile a C++ file the compiler has to read and process thousands of lines from these header files. But external libraries don't change and you can save a lot of time if you only process these files once and save the result.

A precompiled header is simply a bunch of header files that has been processed to an intermediate form that later can be used by the compiler again and again.

Precompiled headers in Visual C++

In Visual C++ it is customary to #include all your non-changing header files in stdafx.h. You then instruct the compiler to create the precompiled header stdafx.pch while compiling stdafx.cpp which does nothing but include stdafx.h. If you want to use the precompiled header in another .cpp file you have to include stdafx.h as the first include file and the instruct the compiler to use stdafx.pch for your precompiled header.

If you get an error about not including stdafx.h you simply have to instruct the compiler to not use a precompiled header for that particular source file. (Or you can include stdafx.h.)

Precompiled header settings for individual source files

Visual C++ allows you to control the compiler settings for the entire project and for individual files. To access individual properties you select the source file in the solution explorer, right click it and select Properties from the context menu. The options for precompiled headers are found at Configuration Properties => C/C++ => Precompiled Headers. If you modify these settings you will often want to do that for all configurations (e.g. Debug and Release).

When you are using precompiled headers you will have a setting for the entire project that instructs the compiler to use stdafx.pch for the precompiled header. The stdafx.cpp will have an individual settings that instructs the compiler to generate stdafx.pch, and if you have some source files that doesn't include stdafx.h you can set individual settings on these to not use precompiled headers.