Ingesting dangerous levels of water is a problem faced most frequently by long-distance runners. One study found that as many as 1 in 6 marathon runners develop water intoxication.
This happens when a person drinks too much water in too short a time which stresses the kidneys.
The kidneys are only capable of processing about 800-1000 ml of water per hour. When a person drinks too much water the kidneys cannot keep up. This disrupts the normal balance between salt and water in the blood and forces excess water into your cells.
For some cells, like muscle and fat cells, this is not an issue as they have the space to expand. But for the cells of the brain, which live within the boney enclosure of the skull, it can be dangerous. Patients who suffer water intoxication may experience headaches, confusion, coma, or in extreme cases death.
The above video goes into depth about water intoxication.
Source: National Institutes of Health