The data displayed on the client computer depends on the intended use. Different kind of radar displays exist for different kind of Air Traffic Controllers (ATC).
For example: VFR controllers, the ones that generally first comes to mind when we think of air traffic controllers, and who primarily direct traffic by looking outside through the tower's glass panes, work directly on airport fields. To assist them in times of low visibility, they generally rely on airport ground surface movement radar (SMR). This allows them to see a general layout of the airport, along with any moving vehicle, airplane or person. Data displayed includes raw digitized video, which is a graphical depiction of the radio wave bouncing off the object, (the blip we often see in war movies), along with an ID tag containing the object's velocity, direction, registration, etc.
The other other main branch of ATCs are IFR controllers. They work in enclosed buildings across the country, and need not be close to any airports. Everything they see and hear comes to them through radar and radio links. Their radar display clients do not show the layout of one airport, but rather a portion of an airspace they are responsible for, along with any routes and airways that cross them. Weather is also overlayed (cloud and storm formations), so as not to direct traffic in danger zones. Aircraft tags contain similar data, including transponder code, flight plan number, altitude, etc.