A displacement wave was an artificially-generated, highly-energetic phenomenon, characterized as a polarized magnetic variation, used by the advanced alien being known as "the Caretaker" to transport ships to the Delta Quadrant.
In 2371, the Caretaker used this technique to transport a number of vessels to his location, in an attempt to find a lifeform genetically compatible with himself, in order to procreate to produce an offspring capable of continuing his mission of caring for the Ocampa. Among the vessels transported to the Delta Quadrant were Chakotay's Maquis ship, the USS Voyager, the USS Equinox, a Cardassian Galor-class vessel, and the Dreadnought missile. (VOY: "Caretaker", "Dreadnought", "The Voyager Conspiracy", "Equinox")
In the year 2267, more than a century earlier, another form of displacement waves were detected when the USS Enterprise was approaching and then in orbit around the Guardian of Forever planet. Commander Spock reported to Captain James T. Kirk that that the ship was passing through ripples in time. Kirk then ordered Lieutenant Uhura to report to Starfleet Command that something or someone down on that planet was causing turbulent waves of space displacement. When Kirk asked Spock again about whether the Enterprise should stay in orbit to investigate, Spock told Kirk that it was of very huge scientific importance that they maintain orbit to study the waves. As the landing party would soon discover the waves were caused by the Guardian of Forever, a time portal like device that refused to answer Kirk's question as to whether it was a being or a machine. (TOS: "The City on the Edge of Forever")