What is the purpose of a .cmake file?

You can include it with the include command. Similar to how other languages allow you to split source files into modules or header files, they can contain function definitions, macros which can then be reused across multiple CmakeLists.

See https://cmake.org/cmake/help/v3.0/command/include.html

Note that you can actually include any file, but a .cmake extension is commonly used.

CMake input files are written in the "CMake Language" in source files named CMakeLists.txt or ending in a .cmake file name extension. https://cmake.org/cmake/help/latest/manual/cmake-language.7.html

This means they're one and the same thing. "CMakeLists.txt" is simply the default name. If you decide to split the code (CMake is technically just another interpreted language) into separate files/modules (that you can include into each other), they obviously can't all have the same name, so you would use the ".cmake" extension. Theoretically, you could call "CmakeLists.txt" as "CmakeLists.cmake", but then cmake won't be able to find it by default, so you'd have to pass the filename as a command-line argument. So it is just a difference of naming conventions. Everything you can put in one file, you can put in the other, and vice-versa.

Within this file you can define functions of macros which can be used in your CMakeLists.txt file. But there are some more other applications for .cmake files. For example if you want to provide a library or tool they should at least contain a <name>Config.cmake so that your library can be used with the find_package() command. Further information can be found in CMake Wiki