Plain English Meaning
CAT III is the lowest-visibility category of ILS approach. The aircraft, the pilots, and the airport ground equipment all have to be specially approved for it, and most CAT III landings are flown by the autopilot all the way to touchdown because the pilot may not be able to see the runway until the wheels are almost on it.
Full Definition
A precision instrument approach and landing classification permitting operations to runway visual ranges (RVR) below those allowed in Category II. CAT III is subdivided into CAT IIIa, IIIb, and IIIc, with progressively lower or no decision height (DH) and progressively lower RVR , down to zero visibility in . CAT III require specially certified (typically or a fail-/fail-passive ), a , and a CAT III–certified facility with the ground infrastructure and protected .