Dawg and dogg are alternate spellings of dog, often applied to close friends. They convey a sense of solidarity, friendship, and usually fierce loyalty.
The "dogg" spelling variation probably originated from hip hop heavyweight Snoop Dogg, with whom it is virtually synonymous. Other possibilities include Swamp Dogg the psychedelic/soul singer, who predates Snoop by a number of years.
Dawg is also associated with the mascot or fans of the University of Georgia Sports teams.