Autoguiding is the process of using an additional telescope (a "guide scope") and camera (a "guide camera") that are attached to the main telescope and are dedicated to tracking the movement of the objects in the sky with the Earth's rotation.
GoTo equatorial mounts do a great job, but tracking errors usually occur if you are imaging for periods longer than 45-60 seconds (depending on the kit).
Autoguiding allows your telescope/camera to more accurately track astronomical objects for longer exposures.