A personality profile was an analysis of one's personality, either formal or informal.
According to Deanna Troi, Lutan's personality profile revealed he had "an abnormally high need for achievement." She explained his kidnapping of Natasha Yar in 2364 by adding that she was a difficult prize to capture. (TNG: "Code of Honor")
Starfleet kept personality profile analyses on its personnel. In 2366, when attempting to refine his holoprogram of Leah Brahms, Geordi La Forge asked the USS Enterprise-D's computer for a personality for her. The computer responded with a personality profile analysis dated stardate 40056. (TNG: "Booby Trap")
While attempting to create a Emergency Medical Hologram Replacement Program with Tom Paris, Harry Kim discussed the need for further additions to the program beyond medical knowledge, including a personality profile. Paris admitted he'd been considering it, adding that they ought to make this one more pleasant than The Doctor. (VOY: "Message in a Bottle")