What it means
River stage is an important concept when analyzing how much water is moving in a stream at any given moment. Stage is the water level above some arbitrary point, usually with the zero height being near the river bed, in the river and is commonly measured in feet.
For example, on a normal day when no rain has fallen for a while, a river might have a stage of 2 feet (baseflow conditions). If a big storm hits, the river stage could rise to 15 or 20 feet, sometimes very quickly. This is important because, from past records, we might know that when the stage hits 21 feet, the water will start flowing over its banks and into the basements of houses along the river -- time to tell those people to move the dog's bed upstairs!
The U.S. Geological Survey uses the term "gage height" (measured in feet) when referring to the height of water in streams.