I'd like a high level description of what it is, and what operating systems need to do in order to support it in virtual machines.
From the VirtualBox documentation, mouse pointer integration means:
To overcome the limitations for mouse support that were described in Section 1.9.2, “Capturing and releasing keyboard and mouse”, this provides you with seamless mouse support. You will only have one mouse pointer and pressing the Host key is no longer required to "free" the mouse from being captured by the guest OS. To make this work, a special mouse driver is installed in the guest that communicates with the "real" mouse driver on your host and moves the guest mouse pointer accordingly.
This essentially means that you can use the guest like any other application, instead of having to switch back and forth between the guest and the host.
In order for a guest OS to support this, it will need to support installing Guest Additions. A list of such OS's is available on the VirtualBox website.