Civilian clothing was any clothing item worn by civilians, or off duty military personnel.
In 2063, Jean-Luc Picard requested mid-21st century civilian clothing from USS Enterprise-E's computer as members of his crew prepared to head down to Earth. (Star Trek: First Contact)
In 2151, Jonathan Archer recommended an impregnated Trip Tucker wear civilian clothing for the duration of his condition, as it would help hide the bulge. (ENT: "Unexpected")
In 2369, upon DeSeve's return from his Romulan defection, William T. Riker ordered him to dress in civilian clothes, saying he didn't want to see DeSeve in a Romulan uniform anymore. (TNG: "Face Of The Enemy")
In a deleted scene from ENT: "The Expanse", Hoshi Sato decided to send her off-duty clothes to her mother in exchange for new ones in order to "upgrade my civvies".