Because a template isn't compilable code until it's instantiated with concrete types, and the compiler needs the full definition visible at each point of instantiation to generate that code. If you put a template's body in a .cpp, other translation units see only a declaration, the compiler has nothing to instantiate from when they use it, and you get "undefined reference" link errors for the specific instantiations. Putting the definition in a header makes it visible everywhere it's used, so each translation unit can instantiate what it needs. This is why the STL and most template libraries are header-only. (There are workarounds like explicit instantiation in a .cpp for a known, fixed set of types, but the default and idiomatic approach is header-only.)
C++ for Embedded · Interview question
Why must template definitions go in header files?
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From the lesson
Templates: The Basics
Write a function or class once and have the compiler stamp out a type-specific version for each use: generic code with zero runtime cost, plus the code-bloat tradeoff to watch.