The fossae have been tentatively identified as outflow channels, but their origin and evolution remain ambiguous. It has been proposed that water may have been released into the troughs as a catastrophic flood due to subsurface ice melting following a large bolide impact. (wikipedia entry)
A fossa is a long, narrow, shallow depression. On Mars they are named after the nearest named albedo feature on the Schiaparelli or Antoniadi maps.