Anti-gravity refers to the state in which an object defies the laws of gravity.
The cloud city Stratos was built, by the Ardanans, above the surface of the planet Ardana, centuries prior to 2269. The city was described by Spock as "the finest example of sustained anti-gravity elevation [he had] ever seen." (TOS: "The Cloud Minders")
During the 23rd and 24th centuries, the Federation employed anti-gravs and later anti-grav sleds to assist in the moving of large or bulky items. (TOS: "The Changeling"; TNG: "Hollow Pursuits", et al.)
At the same time it was not uncommon to see anti-gravity wheelchairs in use by disabled persons. (TOS: "The Menagerie, Part I"; TNG: "Too Short a Season", et al.) Jadzia Dax, via the Dax symbiont, had been familiar with this type of technology as early as the late 22nd century. (DS9: "Melora")