Artist Circle and Gold Circle are terms that event-organizers use to differentiate seating areas. These seats are usually closer to the front and center (i.e. closer to stage, hence "Artist Circle"), and are therefore higher value (hence "Gold Circle"). They are priced accordingly.
Each event arranges seating differently, and may add its own specific meaning to these terms. For these details, check both Info and Pricing on the event page.
If the event has reserved seating for one or more price levels, it may also have a seating chart.
See also: Where can I find a seating chart?