The core virtualbox is open source and free, but the guest tools extension pack is closed and commercial. Under restrictive use cases you are allowed to install the guest tools for personal use for yourself and not need to pay for a license. But even so much as installing it for someone else is a license violation and Oracle expects you to pay for that.
No guest tools extensions means you have no drivers for the guest VM, no shared folders, no mouse/window integration, no accelerated 2d or 3d graphics nor resolutions over 1024x768 vesa.
Whom ever installs the guest tools extension is the ONLY person legally allowed to run that copy of virtualbox afterwards (following the legal agreement when you downloaded it at least.)
If you install virtualbox and the guest extensions on a PC for your mom, mom isn't licensed to run it and Oracle wants a paid license in that case.
Installing virtualbox via scripts including the guest extensions requires a license for each install, even if you are the one using a copy.
(Academic use is somewhat excluded last I saw, but not being in academia I don't know any of those details)
There is an open source version of the guest tools, at least for Linux guests (maybe others by now.)
I'm not sure what features it lacks or differences in the drivers, but they are made by a different development team unrelated to sun/oracle.