When a pilot receives the message : THE RUNWAY IS STERILE, what is the meaning?
A "sterile runway" indicates that all traffic has been cleared from the runway.
This can include both traffic currently active on the runway as well as potentially other inbound traffic on approach, or even elsewhere on the tarmac - if it is deemed disruptive.
A sterile runway is often used in emergency situations, such as when an airplane is coming in for an emergency landing. For the safety of both that plane as well as the others, the runway is cleared of any traffic.
That said, this term is not exclusive to emergencies. For example, the FAA requires 250 feet on either side of a runway to be clear of airplanes when a Commercial Airplane lands. An airport that is smaller and has tight taxiways might have an aircraft taxiing closer than that. To be within FAA compliance, they would need to ensure that the runway was sterile and that there were no active planes taxiing within that 250 feet at the time of the commercial plane landing. An example of this rule being observed includes this notice posted by Friedman Memorial Airport in Hailey, ID, where they adjusted their procedures in response to FAA determinations in order to accommodate commercial traffic and maintain a "sterile runway".
It means that aircraft are not allowed to takeoff/land in that runway. From a British Antartic Survey Document on the Rothera Research Station:
BAS procedures require a sterile runway and airspace at Rothera for all periods where the BAS DASH 7 has passed PNR until it has landed. Aircraft will NOT be allowed to takeoff, land, hold in the overhead or the vicinity of the airfield during this period.