In short, computer magic.

MOOC courses record literally everything you do when logged into the course. Every mouse click, pause, screenshot, going back to a previous session - you name it. It depends on the course but you'd have to at least complete and pass all tests and quizzes. Some courses are linear with one module available at a time, only being able to progress until the module is completed and passed, some have all available at once. Some courses you have to complete all the exercises and pass the tests, or watch all the lectures and pass the tests. It depends on how the course has been designed. The computer tracks your progress and when you've completed the course to the computers specifications, you get a completion certificate.