Plain English Meaning
It means you, and only you, are flying the airplane — your hands and feet are on the controls, and nobody else is helping fly. Time logged this way counts toward the flight hours the FAA requires for licenses and ratings.
Full Definition
A regulatory term used in pilot logbooks and FAA recordkeeping to describe the pilot who is personally operating the flight controls of an aircraft, with no other pilot touching or sharing those controls during that time. Flight time logged as sole manipulator counts toward aeronautical experience requirements for ratings and certificates, provided the pilot is rated (or appropriately authorized) for the category and of aircraft being flown.