Unity requires a 3D card and if you have one, a 3D driver. Its window
manager is Compiz which uses compositing. Unity 2D does not require a 3D
card or driver. It is written a different language (QT) and uses a
different window manager, Metacity. This may be Greek to you (or not) but
basically any system will choke at its weakest link. If your graphics card
is not up to it or is using the wrong driver it will affect performance
negatively.

If you have a 3D card and want to use Unity then go to Additional Drivers.
Just start typeing it in the box in Dash and it will come up with it after
three letters or so. Once you open additional drivers it will say if their
are more suitable ones. Not active means that you may have a driver but it
is not in use. You will need to activate it and reboot. If one is available
but not installed then you will have to install and reboot. Potential
problem: after rebooting you cannot get in. Reboot and choose the previous
kernel then remove the offending driver.