A one time modification of an existing zoning law. A Zoning Variance is essentially a bending of the zoning laws in a city or town to accommodate the request of someone trying to renovate their home.

You'll often hear about disputes involving zoning variances, either a renovation blocking someones view or changing the general feel of the neighborhood and potentially diminishing the real estate values of the area.

This Old House has an interesting article involving zoning variance:

http://www.thisoldhouse.com/toh/article/0,,259428-3,00.html