In hydrologic terms, a water-carved channel or gully in arid country, usually rather small with steep banks, dry most of the time, due to infrequent rainfall and the shallowness of the cut which does not penetrate below the level of permanent ground water.
A large waterway with no water in it except when it rains heavily and then the water crashes through the arroyo in giant waves. You may never see an arroyo run, but if you do, for God's sake stay away from it.
An arroyo, also called a wash or draw, is a usually dry creek bed or gulch that temporarily fills with water after a heavy rain, or seasonally. As such, the term is similar to the word wadi. Arroyos can be natural or man-made.