I recently had a class project where I had to make a program with G++.
I used a makefile and for some reason it occasionally left a .h.gch file behind.
So
Other answers are completely accurate with regard to what a gch file is. However, context (in this case, a beginner using g++) is everything. In this context, there are two rules:
Never, ever, ever put a .h file on a g++ compile line. Only .cpp files. If a .h file is ever compiled accidentally, remove any *.gch files
Never, ever, ever put a .cpp file in an #include statement.
If rule one is broken, at some point the problem described in the question will occur. If rule two is broken, at some point the linker will complain about multiply-defined symbols.