This is actually a lowlands Scottish term now popular in the general Pagan community.

In the Northern Hemisphere (Europe, USA, Canada), to walk widdershins is to walk to the left or counter-clockwise within a compass round.

It is thought in some traditions that moving counter-clockwise helps to dissipate energy and is used during such rites as the purification of an area or the inside of a house because it helps to chase away negative energy. At the end of a compass session, walking widdershins is used in taking down a compass, as it helps to unlock the energy field to allow invited spirits to more easily depart to their realms.

In casting a magic spell against the occupants of a house, the witch would walk widdershins around the outside of the house as part of the ritual.

Within a laying a compass, a small opening may be made withershins with an athame or wand, to allow someone to leave or enter, then the opening is closed again deosil. At the end of a compass session, walking withershins is used in taking down a circle, as it helps to unlock the energy field to allow invited spirits to more easily depart to their realms.

Just to be confusing, some traditions in Trad Witchcraft in the Northern Hemisphere hold that widdershins supports energy and deosil dissipates energy.  You should follow your tradition. If you have no specific tradition, use the more popular counter-clockwise direction in the Northern Hemisphere.

The opposite of widdershins is deosil.

In the Southern Hemisphere (Australia, South Africa, New Zealand) the opposite is true. Widdershins is clockwise and deosil is counter-clockwise (anti-clockwise).