In cases of famous masters like Laozi, Zhuangzi, Mozi, Sunzi, Kong Fuzi, etc. the suffix -子 is translated as "master" or sometimes "great teacher." Otherwise it indicates offspring or related concepts: child, descendant, diminutive, egg, seed, youth, sub-, subatomic particle, etc.
What is the etymology from one meaning to the other? I have a guess, but I'll put it in the comments below to not influence anyone who doesn't want to be influenced by my perhaps incorrect (and certainly unsubstantiated) thinking.