What does "radar contact" mean in ATC calls?
The FAA's Pilot/Controller Glossary gives both US and ICAO definitions:


  RADAR CONTACT- a. Used by ATC to inform an aircraft that it is identified on the radar display and radar flight following will be
  provided until radar identification is terminated. Radar service may
  also be provided within the limits of necessity and capability. When a
  pilot is informed of “radar contact,” he/she automatically
  discontinues reporting over compulsory reporting points. [...]
  
  b. The term used to inform the controller that the aircraft is
  identified and approval is granted for the aircraft to enter the
  receiving controllers airspace. (See ICAO term RADAR CONTACT.)
  
  RADAR CONTACT [ICAO]- The situation which exists when the radar blip
  or radar position symbol of a particular aircraft is seen and
  identified on a radar display.
  
  RADAR CONTACT LOST- Used by ATC to inform a pilot that radar data used to determine the aircraft’s position is no longer being
  received, or is no longer reliable and radar service is no longer
  being provided. The loss may be attributed to several factors
  including the aircraft merging with weather or ground clutter, the
  aircraft operating below radar line of sight coverage, the aircraft
  entering an area of poor radar return, failure of the aircraft
  transponder, or failure of the ground radar equipment.


Note that this is not a universal term, Canada uses "radar identified" instead. Their equivalent of the P/CG is the Glossary for Pilots and Air Traffic Services Personnel:


  “Radar identified”
  
  An expression used by ATC to inform the pilot of an aircraft when radar identification is established.
  
  Fr: « Identifié radar »


And:


  “Radar contact”
  
  U.S.: Expression for: “Radar identified”