Sulfur water is a condition where the running water contains a high amount of hydrogen sulfide

Hydrogen sulfide

Hydrogen sulfide is the chemical compound with the formula . It is a colorless, very poisonous, flammable gas with the characteristic foul odor of expired eggs perceptible at concentrations as low as 0.00047 parts per million...

 gas that escapes into the air when the plumbing line is opened, giving a distinct "rotten egg" smell.

Cause

The condition is not dangerous, but indicates a high level of sulfate-reducing bacteria

Sulfate-reducing bacteria

Sulfate-reducing bacteria are those bacteria and archaea that can obtain energy by oxidizing organic compounds or molecular hydrogen while reducing sulfate to hydrogen sulfide...

in the water supply. This may be due to the use of well water, poorly treated city water, or water heater contamination.

Treatment

Treatment for sulfur water is turning up the temperature setting on the water heater to over 140°F and running it for several hours, letting others know you have scalding water running in your pipes, and then flushing the water heater clean. The heat is supposed to kill the bacteria. One should also get a good water filter to remove all mineral and chemical impurities at the tap.