Primary radar sends out a strong signal from the ground which is bounced back off the aircraft and received by the same equipment on the ground which then derives the position of the a/c and is displayed on a radar screen. Whether as a raw return (i.e. like the movies with the sweeping glow and fading) or as a synthesized picture (a little cross or box or other symbol representing the raw return on a digital picture).
Secondary radar sends out a weaker signal as it only needs to be received by the aircraft, not reflected back. The transponder onboard the a/c is interrogated by this signal and then sends back a reply which is received by the ground based equipment. As Meister poinst out this can be mode A which is callsign data, allowing for easier ID
than primary alone, or (as most a/c do) can have mode C also which gives a height readout from the a/c altimeter. This allows ATC to separate a/c easier as they can see levels of a/c without asking for reports.
Mode S is the next big development and will allow every a/c in the world to have a discrete secondary radar ID
, instead of an allocated four digit transponder squawk. And will allow ATC to see almost all information that may be required, such as climb rates, indicated air speed, even the level the pilot has set on autopilot, allowing us to check if the pilot has entered the correct level after his clearance. You would not believe the number of 'Level busts' because pilots get levels and headings mixed up, even after reading instructions back correctly. Pilots have a lot of numbers to think about and look at in front of them so I imagine its easily done.