A unique copy of a dungeon/area created when you and your group enter that dungeon/area. Only you and your group will be in your copy of the dungeon. Another group that enters the same area will enter their own copy of the dungeon if it is a single grouped instance. Other instances may allow groups to play versus each other in a PvP form. An instance like this will be found in the Border Kingdoms in Age of Conan.
Instances are also used for ordinary game zones to keep the number of people in each area manageable. There are multiple copies of each zone and you get assigned to one by the server. It is possible to change which instance you are in using the select instance feature so that you can group with and play with friends and guild members.
In Tortage you can choose to play in Night mode. When you do so you play in your own instance of the city and it surroundings.