An anticyclonic tornado is a tornado which rotates in a clockwise direction in the Northern Hemisphere and a counterclockwise direction in the Southern Hemisphere. The term is a naming convention denoting the anomaly from normal rotation which is cyclonic in upwards of 98 percent of tornadoes. Many, but not all, anticyclonic tornadoes are smaller and weaker than cyclonic tornadoes, forming from a different process.
Most strong tornadoes (the classic conception of a tornado) form in the inflow and updraft area bordering the updraft-downdraft interface (which is also near the mesoscale "triple point") zone of supercell thunderstorms. The thunderstorm itself is rotating, with a rotating updraft known as a mesocyclone, and then a smaller area of rotation at lower altitude the tornadocyclone (or low-level mesocyclone) which produces or enables the smaller rotation that is a tornado. All of these may be, but aren't always, quasi-vertically aligned continuing from the ground to the mid-upper levels of the storm. All of these cyclones and scaling all the way up to large extratropical (low-pressure systems) and tropical cyclones rotate cyclonically. Rotation in these synoptic scale systems stems partly from the Coriolis effect, however, thunderstorms and tornadoes are too small to be significantly affected. The common property here is an area of lower pressure, thus surrounding air flows into the area of less dense air forming cyclonic rotation. The rotation of the thunderstorm itself is induced mostly by vertical wind shear.