Plain English Meaning
The controllers who take charge of an aircraft as it gets close to a busy airport. They line up the arriving traffic, tell pilots which headings and altitudes to fly, clear them for the approach, and then pass them to the tower for landing.
Full Definition
An air traffic control facility that provides radar and non-radar services to aircraft arriving at, departing from, or transiting the airspace surrounding one or more busy airports, typically from about 30 to 50 nautical miles out and up to around 10,000 feet. Approach control sequences and separates arriving traffic, issues vectors and altitude assignments, clears aircraft for instrument approaches, and hands them to the airport's tower for landing.