An artifact is any undesired visual effect such as tearing or jittering.
Jittering is a term used to describe what happens when two frames are being displayed alternately but are misaligned by one pixel.
Tearing is a term used to describe what happens when an applications frame rate is out of sync with the display refresh rate, resulting in the top and bottom halves of the screen displaying different frames seperated by a visible tear.
There are many other types of artifacts, such as left over pixels due to poor clipping and coloration errors resulting from inappropriate palette modifications.