They need to be visible for the compiler when they are instantiated. That basically means that if you are publishing the template in a header, the definitions have to be visible by all translation units that include that header if you depend on implicit instantiation.
They need not be defined in the header if you are going to explicitly instantiate the templates, but this is in most cases not a good idea.
As to the reason, it basically boils down to the fact that templates are not compiled when the compiler parses the definition, but rather when they are instantiated, and then they are compiled for the particular instantiation type.
