An artesian well is one with pressure behind it. When a well is drilled and the level of the water comes up higher than the length of the hole that was drilled, it's called an artesian well. A well where the pressure is high enough so that the water will come above ground level without pumping is called a flowing artesian well.
Here in Olympia we have a history of many flowing artesian wells and springs. The water comes from an aquifer deep beneath the ground. This water has been tested to be approximately 1,000 years old.
Water flows from the recharge zone in the neighboring hillsides and is slowly filtered through layers of sand and clay. In Olympia, the aquifer ultimately drains into the Puget Sound.
Here are some links of interest:
:WA Department of Ecology - Olympia artesian wells a valuable asset: