Plain English Meaning
Skywatch is a piece of equipment fitted in some general aviation aircraft that actively looks for nearby airplanes by pinging their transponders. It then shows where that traffic is on a screen and warns you when something is getting close.
Full Definition
An active traffic advisory system manufactured by L3 Avionics (originally BFGoodrich) that interrogates the transponders of nearby aircraft and displays their range, relative bearing, and altitude to the pilot, along with aural alerts when traffic is assessed as a threat. It is a TAS (Traffic Advisory System) — it provides traffic advisories only, not resolution advisories like the larger TCAS II found in airliners.