Definition
CLEARED FOR THE OPTION
ATC authorization for an aircraft to make a touch‐and‐go, low approach, missed approach, stop and go, or full stop landing at the discretion of the pilot. It is normally used in training so that an instructor can evaluate a student's performance under changing situations. Pilots should advise ATC if they decide to remain on the runway, of any delay in their stop and go, delay clearing the runway, or are unable to comply with the instruction(s).
Source: FAA Pilot/Controller Glossary (verbatim from the Federal Aviation Regulations).