Run has many dictionary definitions such as "moving swiftly by foot". See Running, and "Run" in Wiktionary.
A run in a stream or river is a fairly smooth flowing segment or part of the flow differentiated from a pool where the water is deeper and slower moving, and a riffle where the flow is shallower and more turbulent.
A death run is a run that is faster than 333 beats per minute. An example is a 392-bpm run at the end of the song Healing Vision Angelic Mix from DDRMAX: Dance Dance Revolution 6thMIX.
Run is a term used commonly in Role Playing Games to flee a battle, not gaining any experience. Run options are often limited (such as not being able to run from boss battles, faster enemies, and costing you money).