The correct terms are: geyser, eruption, heated groundwater.
On this picture we can see an underground reservoir of water, bellow which there's source of heating. The water goes vertically towards the surface, and shoots out in the air.
These are characteristics of a geyser. The water is heating deep into the ground by the magma bellow it. Because of the heating, the water has very high pressure. As it goes upwards, because of the high pressure, the water shoots up into the air. The water is hot.
These places are often seen as tourist attractions, and the most famous ones are located in the Yellowstone National Park in the northwestern part of the United States.
