While Continuum in its current form doesn't let you do manipulate windows like you would in a normal desktop, it does allow you some form of multitasking by using your Continuum-enabled Windows 10 Mobile device (such as the Lumia 950 and Lumia 950 XL) as a secondary screen.
When you first connect your phone to a Continuum display dock or wirelessly connected display, the first thing it will do is transform your phone's screen into a touchpad to control the mouse on the connected screen. What isn't immediately obvious is that you can still control the phone normally, allowing you to use the phone alongside the attached station. Tap any of the navigation buttons (start, back, search) to exit out of the touchpad mode. When outside of touchpad mode while docked, a bar on top of the screen will indicate what you are connected to and that you are in Continuum mode. Tapping that bar resumes touchpad control.
The start menu on the desktop is the same as the start screen on your phone, so you can call upon any app using either screen. This is important because which screen you summon the app from dictates where it shows up. Invoking an app that's already being shown on another screen will transfer the app from the other screen to the calling device.
Through this, you can use up to two apps simultaneously. Bear in mind only apps that are designed for Continuum can be run in this manner. Apps that aren't designed for Continuum will be faded out and you'll be unable to invoke them.
It's also important to note that for any app that controls music, such as the Groove Music app, the music will be heard on the connected speakers, not on the phone itself, regardless of where you invoke the app from.
Watch Zac's hands-on demonstration for more info on how to use Continuum.