No need to install wiring!
Wireless burglar alarms operate differently from their hard-wired counterparts in that the component parts (control panel, sensors and alarm) communicate via radio signals, rather than electrical wired connection across the whole system. Beyond this fundamental difference, the actual methods for detecting intrusion are common to both. In the majority of cases this is based on motion detection using Passive Infrared technology (which actually works by sensing the increased body heat of an intruder), sometimes combined with magnetic sensors attached to doors or windows that trigger an alarm when they are opened.
So what are the advantages of wireless burglar alarms? Essentially all the benefits you can think of arising from the absence of wires, including that:
there is none of the disruption (and potential damage) involved in installing a hard-wired alarm (e.g. removing floorboard, drilling, re-plastering etc.);
the sensors can be placed almost anywhere – location is not dictated by complex wiring issues;
they can be easily removed and re-installed in a different building (they are widely used by tenants in rented accommodation where landlords will not allow alterations);
additional sensors can be added easily, e.g. if a building is extended or the security level needs changing.