Conventions.
Historically, the suffix for a C++ source file was .C.
This caused a few problems the first time C++ was ported
to a system where case wasn't significant in the filename.
Different users adopted different solutions: .cc,
.cpp, .cxx and possibly others. Today, outside of the Unix
world, it's mostly .cpp. Unix seems to use .cc more often.
For headers, the situation is even more confusing: for whatever
reasons, the earliest C++ authors decided not to distinguish
between headers for C and for C++, and used .h.
This doesn't cause any problems if there is no C in the project, but when you
start having to deal with both, it's usually a good idea to
distinguish between the headers which can be used in C (.h)
and those which cannot (.hh or .hpp).
In addition, in C++, a lot of users (including myself) prefer keeping the template
sources and the inline functions in a separate file. Which,
while strictly speaking a header file, tends to get yet another
set of conventions (.inl, .tcc and probably a lot of
others).
In the case of headers it makes absolutely no difference to the compiler.
In the case of source files different endings will cause the compiler to assume a different
language. But this can normally be overridden, and I used .cc
with VC++ long before VC++ recognized it as C++.