‘Bbang’ means bread in Korean. It’s a nickname given to him by the boys and the Secret members and is used between the TS family. We don’t think there’s a special meaning behind it; they probably call him that only because it sounds cute. The nickname was first mentioned on Twitter by Himchan:
“I’ll tweet dizzily a message that only you know about with a nickname filled with my affection, happy birthday bbang♥”
And later on he talked about it on Starry Night.