North Carolina is nicnknamed the "Tar Heel State", and athletic teams at the University of North Carolina are also called "Tar Heels. Sources including the University of North Carolina website (http://www.unc.edu/about/traditions.html) and the website of the state library of North Carolina (http://statelibrary.dcr.state.nc.us/nc/symbols/symbols.htm#nickname) explain the origin of this nickname: In 1629, King Charles I of England "erected into a province," all the land from Albemarle Sound on the north to the St. John's River on the south, which he directed should be called Carolina. The word Carolina is from the word Carolus, the Latin form of Charles. When Carolina was divided in 1710, the southern part was called South Carolina and the northern, or older settlement, North Carolina. From this came the nickname the "Old North State." Historians have recorded that the principal products during the early history of North Carolina were "tar, pitch, and turpentine." It was during one of the fiercest battles of the War Between the States, so the story goes, that the column supporting the North Carolina troops was driven from the field. After the battle the North Carolinians, who had successfully fought it out alone, were greeted from the passing derelict regiment with the question: "Any more tar down in the Old North State, boys?" Quick as a flash came the answer: "No, not a bit, old Jeff's bought it all up." "Is that so; what is he going to do with it?" was asked. "He's going to put on you-un's heels to make you stick better in the next fight." Creecy relates that General Lee, upon hearing of the incident, said: "God bless the Tar Heel boys," and from that they took the name (Adapted from Grandfather Tales of North Carolina by R.B. Creecy and Histories of North Carolina Regiments, Vol. III, by Walter Clark). The above is quoted directly from the state library page cited above.

During the colonial days the tar industry was big in North Carolina because of the insane number of trees perfect for getting tar. The tar was put on hulls of ships to waterproof them. During the messy production of the tar, the bottom of the workers feet would get covered in it. Thus, the name tar heels. The name was not highly used until the incident during the civil war that is described in the other answer.