The Georgia District Tartan was officially recognized as a symbol of Georgia in 1997. Quote from Tartans of Scotland:

"The Georgia District Tartan commemorates the founding of the State of Georgia and combines elements in the design associated with its historic past. General Oglethorpe commanded the Highland Independent Company of Foot which, in 1746, wore the Black Watch tartan. Captain John 'Mohr' MacIntosh is remembered in the MacIntosh red. Georgia tartan is much in evidence at the annual Stone Mountain Highland Games held in Atlanta, Georgia's capital."
 

Tartan refers to fabric woven into plaid patterns representing clans (families) or regions in Scotland.

In old Scotland, the tartan was used for clothing and as a banner or flag. Because a family or community worked the cloth together, their clothing was made of the same patterns, and so a person could be recognized by the Tartan plaid that he wore. Tartans can also be designed as a symbol commemorating a special event or person.

Source:

State Tartan: Georgia Secretary of State
Tartans of Scotland
Scottish Tartans Museum; History

Links:

Cultural Symbols - 50 states