Web Activities are an alternative way to Web APIs to access the hardware in a certain device. Instead of getting an API to speak to the device directly, Web Activities allow you to create an ecosystem of applications on the device talking to each other. For example, instead of trying to access the camera, your app would ask for an image and the users of the device can use their favourite application to take a photo. Instead of asking the users for access to the hardware (which is important in terms of security), you allow them to use applications they already trust to do that. Furthermore, you can register your application as the go-to application for certain tasks in the operating system. You can think of Web Activities as the same process right-clicking on a file in a Desktop OS does: you get several apps as the option to open this file and you have a chance to tell the OS to always use this app from now on for this kind of file. Web Activities allow apps to talk to each other - on the device, without any need of a server in-between. All they transmit from one app to the other is the final data.

More on Web Activities: https://wiki.mozilla.org/WebAPI/WebActivities
More information on the video series: https://developer.mozilla.org/en-US/Firefox_OS/Screencast_series:_App_Basics_for_Firefox_OS