Plain English Meaning
A departure where the controller watches your aircraft on radar and tells you which way to turn and how high to climb, rather than you flying a pre-printed departure path on your own. The controller steers you from the runway out to your planned route by giving you headings to fly.
Full Definition
An IFR departure in which air traffic control uses radar to provide navigational guidance in the form of headings (vectors) to the departing aircraft, rather than requiring the pilot to follow a pre-published departure route. After takeoff, the controller issues specific headings and to guide the aircraft from the onto its of , while its on radar.