The Second Citizen (in my text, "Second Plebian") is actually a cobbler. The "mending of soles" is a clever play on words (soles = souls).
First, his lines read:
A trade, sir, that I hope I may use with a safe conscience,
which is, indeed, sir, a mender of bad soles. (1.1.13-16)
Truly, sir, all that I live by is with the awl. I meddle with no tradesman's matters nor women's matters, but withal I am indeed, sir, a surgeon to old shoes. When they are in great
danger, I recover them. As proper men as ever trod upon
neat's leather have gone upon my handiwork. (1.1.22-26)
The cobbler lines are directed to Flavius and Marullus, who are plotting to kill Caesar (along with others). The cobbler is among the many who have come taken the day off in order to see Caesar. The talk about "souls" therefore makes the pair feel guilty about their impending betrayal. Their treachery is compared to the honest labor of the citizen.