Microsoft was in a big hurry to push their 1 year anniversary updates for Windows 10. Such a hurry they forgot to test the way their new video encoding system would work with the most common webcams on the market. They were trying to make a new video stream system that would allow the webcam to be used by multiple apps simultaneously, but instead they accidentally broke more than half of all Windows 10 users webcams. Also, with this new update (1607), the amount of time users have to uninstall updates has been reduced from 30 days to just 10.
Fortunately you still have time to uninstall this update and keep using your webcam. Go to your Start menu, open Settings, go to Update & Security, and select Recovery. Now click on “Go Back to an Earlier Build,” select Next, and pick a date before the Anniversary update was installed. Of course, you should back up your data and make sure your laptop is plugged in before uninstalling a Windows update, just in case.