The Da (Big) / Xiao (Small) prefixes are direct translations of family honorifics that in the simple case directly indicate the relative age of one family member to another. The more common use for family is with more layers of indirection -- so when referring to my mother's younger sister, I would say "Xiao Ai" (Little Aunt), and when referring to my mother's older sister, it would be "Da Ai" (Big Aunt).
In this case I imagine it was more in a professional context, so "Shi Qiang" -- family name "Shi", given name "Qiang" -- was likely elder or the superior of people around them, so would be called "Da Shi" (Big Shi / Boss Shi). If Shi Qiang were the younger, they'd likely be called "Xiao Shi" (Little Shi / Subordinate Shi).
In this case I imagine it was more in a professional context, so "Shi Qiang" -- family name "Shi", given name "Qiang" -- was likely elder or the superior of people around them, so would be called "Da Shi" (Big Shi / Boss Shi). If Shi Qiang were the younger, they'd likely be called "Xiao Shi" (Little Shi / Subordinate Shi).