The basic concept of SARH is that almost all detection and tracking systems consist of a radar system, so duplicating this hardware on the missile itself is wasted. In addition, the resolution of a radar is strongly related to the physical size of the antenna, in the small nose cone of a missile there isn't enough room to provide the sort of accuracy needed for guidance. Instead the larger radar dish on the ground or launch aircraft will provide the needed signal and tracking logic, and the missile simply has to isten to the signal and point itself in the right direction.
Contrast this with beam riding systems, in which the radar is pointed at the target and the missile keeps itself centered in the beam by listening to the signal at the rear of the missile body. In the SARH system the missile listens for the reflected signal at the nose, and is still responsible for providing some sort of "lead" guidance. The advantages are twofold. One is that a radar signal is "fan shaped" growing larger, and therefore less accurate, with distance. This means that the beam riding system is not terribly accurate at long ranges, while SARH is largely independant of range and grows more accurate as it approaches the target -- the "source" of the signal it listens for. Another addition is that a beam riding system must accurately track the target at high speeds, typically requiring one radar for tracking and another "tighter" beam for guidance. The SARH system needs only one radar set to a wider pattern.
Early SARH systems typically required the tracking radar to continually point at the target, known as "lock on". Electronic warning systems could listen for this signal and thereby alert the target pilot that a missile launch was likely to take place. However advances in the electronics in both the missile tracking systems and the radars have largely eliminated this in modern systems.
SARH is typically not all that accurate. A number of additional systems are then used to "fine tune" the guidance, including additional information coded in the radar signal (phase angle for instance) and typically some sort of proximity fuse and often even a terminal guidance system.