A physical examination, sometimes shortened to physical exam or physical, or also know as a medical examination (medical exam) or check-up, was a full examination that assessed an individual's general health and well-being.
Physicals may be ordered at the discretion of the chief medical officer whenever necessary, including of the captain. Aside from ordered physicals starships also have regular physicals to monitor the regular health of the crew. In the 23rd century these physicals were done quarterly, but by the 24th century they were only performed annually. (TOS: "The Corbomite Maneuver"; TNG: "Allegiance")
Doctor Leonard McCoy conducted a quarterly physical on Captain James T. Kirk in 2266, just prior to the USS Enterprise's encounter with the Fesarius. As he had been unable to complete one on Kirk before this time, he held off informing Kirk about the red alert the ship was under in order to complete the examination first. (TOS: "The Corbomite Maneuver")
In 2371, The Doctor discovered that Ensign Samantha Wildman was pregnant during her annual physical, but she asked him to keep it from Captain Kathryn Janeway, as Wildman wanted to inform her personally. (VOY: "Elogium", "Fury")
In 2375, The Doctor added deep-body scanning with his holographic imager as part of annual physicals on-board USS Voyager, allowing him to create images of his patients down to the subatomic level. Captain Kathryn Janeway, however, did not report for her physical, "as usual," forcing him to track her down in her ready room to administer her physical, with a request to drop by Sickbay at her earliest convenience to undergo the deep-body scan. (VOY: "Latent Image")