Bragg was a horrible general in every sense. His main battlefield tactic seemed to consist of little but frontal assaults, which cost him the lives of thousands of his men for little gain. He lost nearly every battle he fought except for Chickamauga, where his victory mainly came from reinforcements led by Gen. Longstreet sent by Lee. He was a brutal disciplinarian whose own men hated him, he bickered and fought constantly with his subordinate generals (in 1863, led by Longstreet, they sent a letter to Confederate President Jefferson Davis begging him to remove Bragg from command, as he was incompetent to command the army.) As Bragg was personal friends with Davis, Davis kept him on, only to see him get crushed by Grant at Chattanooga a few months later, and Davis had no choice but to relieve him. Davis eventually put Bragg in command of the defenses at Wilmington, where he screwed up again by not sending enough men to Fort Fisher downriver to adequately defend it, and instead kept most of his men at Wilmington where they were useless. When Fort Fisher fell to US Army troops they didn't have to capture Wilmington directly, as the port was effectively cut off from the outside world anyway. There are many stories of how awful he was as a general, and some people at the time seriously thought he was mentally unstable, as he would go off on long rants and tirades when he lost his temper. Not to mention that he fought for the rebellion and for slavery, but even as a military general, his chosen profession, he sucked.
A number of military bases in the South are named after Confederates. As to why Fort Bragg was named after him, I've read that there were not that many famous high-ranking Confederate generals from NC, and so it was named after him basically by default. Surely there is another North Carolinian from some other war that is far more deserving of the honor, one would think.