Global data in a DLL is exactly what it says, data that is global to the DLL. I'm not sure if it's global to all instances of the DLL (say where three programs are running that each load the DLL); the only time I've done DLL programming was in the Windows 3.x days and I think it might have been. (These days I would expect each process to have separate global DLL data but I'd have to check to be sure.)
Static member functions will act like global data, just as they do in executables, and like global data are worth avoiding if you want to be threadsafe. If you have to have global/static data, then you will need to mutex access to that data (again, just as you would have to in an executable).