Activities are like a new set of workspaces for you to switch to. Like let's say you use your laptop for work and for fun at home. At work you use 4 workspaces and plain desktop backgrounds and conky to watch processes. Then when you punch out at work and want to relax you want just one workspace with cycling wallpapers or whatever. You can set up a "work" activity that fits those needs and then a "home" activity that is much simpler for at home. I think of it as like a third dimension for workspaces.
Okay so as I understand it: virtual desktops are additional space that add screen space that you can jump to ; workspaces are like a more malleable version of virtual desktops ; and activities are an additional dimension on top of that with which you can switch between different virtual desktops and/or workspaces configurations.