Running a checklist protocol was the first step of a systems test, a simple diagnostic of a starship's systems that could be run from the Captain's chair by the commanding officer. There were multiple steps to running the checklist protocol as well.
In 2257, Ensign Sylvia Tilly was shadowing Captain Christopher Pike's duties as part of the Command Training Program when he asked her to run a checklist protocol as part of a systems test, though she never started step one due to the distractions of a multidimensional fungal parasite. (DIS: "Point of Light")