Radar is the acronym for Radio Detection And Ranging. A radar emits intensive radio signatures and detects an echoed response. The speed of this signature is approximately at light speed, which makes the emission reach the radar dish in a matter of milliseconds, both under terrestrial circumstances and in deep space (assuming that the distance is low enough). A simple radar sign can detect a target's IFF, class, and name. Based on at least two response echoes, a target's speed or acceleration can be detected.
In FreeSpace, all spacecraft are equipped with sensors and scanners of various degrees of power, which are presumably radar-based. This assumption is based on the existence of radar dish subsystems on certain larger Terran ships, such as the GTD Orion or the GTC Fenris. Their specific advantage is never elaborated on, but presumably they increase the range or accuracy of the vessel's sensors as compared to designs without such accouterments, although they could simply be an old, outdated part of the sensor equipment on those ships, and was not replaced because it wasn't worth the cost.