A principle was a rule, a law, a guideline, or a fact that governed one's conduct.
In 2371, Tom Paris mentioned that his father Owen Paris used to talk to him about the Prime Directive once a year, which Tom likened to a holiday sermon. According to Captain Kathryn Janeway, Owen Paris considered the Prime Directive to be the guiding principle of space exploration. (VOY: "Time and Again")
In an argument with Kira Nerys about his aggressive attitude towards the visiting Karemma delegation, Quark claimed to have principles, but the colonel rejected this as untrue. (LD: "Hear All, Trust Nothing")