Quote from The C++ standard library: a tutorial and handbook:
The only portable way of using templates at the moment is to implement them in header files by using inline functions.
Why is this?
(Clarification: header files are not the only portable solution. But they are the most convenient portable solution.)
Plenty correct answers here, but I wanted to add this (for completeness):
If you, at the bottom of the implementation cpp file, do explicit instantiation of all the types the template will be used with, the linker will be able to find them as usual.
Edit: Adding example of explicit template instantiation. Used after the template has been defined, and all member functions has been defined.
template class vector<int>;
This will instantiate (and thus make available to the linker) the class and all its member functions (only). Similar syntax works for function templates, so if you have non-member operator overloads you may need to do the same for those.
The above example is fairly useless since vector is fully defined in headers, except when a common include file (precompiled header?) uses extern template class vector<int> so as to keep it from instantiating it in all the other (1000?) files that use vector.
Templates need to be instantiated by the compiler before actually compiling them into object code. This instantiation can only be achieved if the template arguments are known. Now imagine a scenario where a template function is declared in a.h, defined in a.cpp and used in b.cpp. When a.cpp is compiled, it is not necessarily known that the upcoming compilation b.cpp will require an instance of the template, let alone which specific instance would that be. For more header and source files, the situation can quickly get more complicated.
One can argue that compilers can be made smarter to "look ahead" for all uses of the template, but I'm sure that it wouldn't be difficult to create recursive or otherwise complicated scenarios. AFAIK, compilers don't do such look aheads. As Anton pointed out, some compilers support explicit export declarations of template instantiations, but not all compilers support it (yet?).