Automation on this shelf runs from a single motor that follows the sky to an instrument that images all night while you sleep, and the steps between are worth separating because they cost very different amounts.
A tracking motor
The simplest automation: one motor turning the polar axis at the sky's rate. It keeps an object in the eyepiece and does nothing else. On an equatorial mount it is often a cheap add-on and it transforms high magnification observing, because you stop nudging and start looking.
Computer control and pointing
Add encoders, a second motor and a database and the instrument finds objects as well as following them. This is what most people mean by an automated or computerized telescope, and it is the level at which the motors begin costing meaningful aperture at a given price.
Fully unattended imaging
At the top, software runs the whole night: it slews, focuses with a motorised focuser, plate solves to confirm the framing, guides, takes a planned sequence and parks the mount at the end. This is a real and popular way to do deep sky imaging and it is a software and mount investment more than a telescope one.
What automation cannot do
Gather more light, resolve finer detail, or improve a night with poor seeing. Every level of automation removes work and none of them changes the physics. That is why the recommendation for a first instrument is so often aperture first: automation makes observing easier and the mirror decides what there is to see.
Questions people ask about telescope
What is an automated telescope?
One that at least tracks the sky, and usually also finds objects from a database. At the top end, software can run a whole imaging session unattended.
Can a telescope track automatically?
Yes, with a driven mount. It is the single most useful piece of automation for visual observing at high magnification.
Does automation improve the image?
No. It removes work. Aperture, optics and the atmosphere decide what the instrument can show.