You normally don't need to know in details the internal format of the Obj files, since they are generated for you. All you need to know is that for every class you create, the compiler generates and Obj file, which is the binary byte code of your class, suited for the OS you are compiling for. Then the next step - linking - will put together the object files for all classes you need for your program in a single EXE or DLL (or whatever other format for the non-Windows OS-es). Could be also EXE + several DLLs, depending on your wishes.
The most important is that you separate the interface (declaration) and implementation (definition) of your class.
Always put in the header file interface declarations of your class only. Nothing else - no implementations here. Avoid also member variables, with custom types, which are not pointers, because for them forward declarations are not enough and you need to include other headers in your header. If you have includes in your header, then the design smells and also slows down the building process.
All implementations of the class methods or other functions should be in the CPP file. This will guarantee that the Obj file, generated by the compiler, won't be needed when somebody includes your header and you can have includes from others in the CPP files only.
But why bother? The answer is that if you have such separations, then the Linking is faster, because each of your Obj files is used once per class. Also, if you change your class, this will change also a small amount of other object files during the next build.
If you have includes in the header, this means that when the compiler generates the Obj file for your class it should first generate Obj file for the other classes included in your header, which may require again other Obj files and so on. Could be even a circular dependency and then you can not compile! Or if you change something in your class, then the compiler will need to regenerate a lot of other Obj files, because they become very tight dependent after some time, if you don't separate.