A geyser is a natural fountain of boiling water. If the water does not jet into the air it is called a hot spring. If it is very muddy water, it is called a mudpool. Sometimes there is only enough moisture to make fumes.
The reason people know about geysers is because they are very dramatic. But they are also rare. They only form over places where there are very hot rocks below the surface, which means they only form in regions where there are active, or near active volcanoes. The area around Yellowstone National Park in NW America, and Iceland are the most famous sites of geysers.
Typically what happens is that cold water, perhaps from a stream or rainwater, seeps down in the cracks in the rock. As it goes down farther, it reaches hot rocks and begins to reach boiling point. But there is more cold water seeping in above the boiling water and this acts like a lid of a pressure cooker. Eventually the boiling water (now well above normal boiling point) is under so much pressure it bursts out through all the cold water above, and that is when you get a geyser.
After a few moments that burst of hot water stops (it literally runs out of steam) and the process starts all over again. That is the reason geysers are active in fits and starts.