Special operations or covert ops were clandestine or covert missions that could not be officially acknowledged due to their sensitive or unsavory nature. In many cases, it involved crossing into enemy territory undetected. Depending on the nature of the mission, these operations may be classified as black and grey ops. Section 31 was considered a Starfleet black ops organization.
In 2369, Captain Jean-Luc Picard was assigned a special operations assignment on Celtris III on a mission to seek and destroy a metagenic weapon. (TNG: "Chain Of Command, Part II") His team included himself, Doctor Beverly Crusher, and Lieutenant Worf, and required several hours of simulated training in the holodeck. (TNG: "Chain Of Command, Part I")
At some point prior to 2380, Beckett Mariner conducted some "some off-the-books grey ops stuff" with Klingon General K'orin. While she never specified the details of their mission, she did note to Brad Boimler that they had worked together on Jaxxa Prime, Vulcan and Earth. (LD: "Envoys")
Following her departure from her work aboard the USS Tikhov, D. Nhan was asked by Federation Security to lead a cleanup task force against the Emerald Chain. Because the posting was a covert ops job, she couldn't tell anyone, and was thus out of contact with her friends aboard the USS Discovery. (DIS: "Rubicon")