Jones means “John’s,” the same idea as Johnson, but in the -s style common in Wales and western England. John (Welsh Siôn) was everywhere; ap Siôn—“son of Siôn”—was routinely written down as Jones once English administrators wanted a fixed surname.
That Welsh pipeline is why Jones feels especially dense in Wales and among Welsh-descended Americans, even though English “John’s” families contributed too. It is a parent’s-name surname, not a place or a trade. Two neighbors named Jones in a phone book need not share a medieval ancestor—only the same popular father’s name frozen into inheritance.