This isn't like Ubuntu's convergence vision with running the same software stack on both the phone and any connected devices nor is it like Microsoft's Continuum. This MaruOS effort is like more Canonical's older (and now defunct) Ubuntu For Android effort whereby connecting your Android device to a monitor or TV would yield a "pure Linux" experience separate from the Android stack.
Currently supported for the MaruOS beta is the Google Nexus 5 smart-phone, which when connected to an external display will load up MaruOS, their derivative of Debian. Android can continue to run on the phone and is independent of the external OS environment. When connected to an HDMI display, Bluetooth keyboard/mice can be used for input.
Unfortunately, MaruOS isn't a free-for-all to try out right now but there is a beta waiting list that interested users must sign up for. If you want to learn more about this effort, visit MaruOS.com.