Definition
An ATC authorization for a pilot to execute any standard or special instrument approach procedure published for that airport. When issued without specifying a particular approach, the pilot may choose which published instrument approach to fly.
Plain English
ATC has given you permission to fly an instrument approach into the airport. If they didn't name a specific one, you get to pick which published approach you want to use.
Context Anchor
Heard during instrument flight when approach control or tower authorizes an aircraft to begin the final charted path toward landing.
Derivation
Cleared comes from an older sense of being free or permitted to proceed. Approach means the act of coming closer. In aviation, the phrase means ATC has permitted the aircraft to proceed with the approved approach toward the airport.
Why Pilots Care
It allows the pilot to descend and navigate toward the runway without needing step-by-step vectors until reaching the missed approach point or landing.
Intuition Check
Cleared does not mean the runway, airspace, or weather is automatically safe. Here, cleared means ATC has authorized the aircraft to fly an approved approach procedure; the pilot still must fly it correctly and stay within required limits.
Example Sentence 1
Approach control radioed, 'November One Two Three Alpha, cleared approach,' so the pilot selected the RNAV Runway 18 procedure and began the descent.
Example Sentence 2
With the approach clearance received, the crew began the descent on the localizer and glideslope.