Taken as a tradesman, the name of "cobbler" is synonymous with shoe-maker (or shoe-repairer in these days of mass-produced sneakers). In the olden-days, the town cobbler was the maker and seller and fixer of footwear, stockings (usually by his wife) and probably also repaired all manner of leather goods if the town didn't have a Leatherman, as he was probably one of the few people who had the necessary tools.
In the days before mass-production (19th century) a pair of shoes would be in a family for years, passed down from wearer to wearer, especially if they were children's shoes. And while they were sturdy and solid, in the days before transit systems as we know them, walking was king and a you'd probably wear through the soles of the shoes once every couple of years. But even though the sole was worn, the rest of the shoe was probably still fine. They would be taken to the town cobbler/shoe-maker and the sole and, if necessary, the heel would be replaced, broken buckles and eyelets replaced, and they would be foot-worthy for another few years.
It was mass-production that effectively killed cobbling as a large-scale trade. With mass-produced shoes it was often cheaper to buy a new pair than repair the old ones, and many shoes were made increasingly of formed rubber instead of sewn leather so repair was difficult at best.
However, there still are a number of cobblers in any reasonably large city for those who enjoy footwear of a caliber that can be repaired. Any decent pair of dress shoes, work boots or sandals can be re-shod and made new without the pain of "breaking in" a new pair of shoes. Any shoe with a sewn-on sole or where the sole is not a formed piece of the shoe itself can probably be repaired if you're willing to pay.
In the days of sneakers with air pumps, it's humbling to think that your grandparents have shoes in their closets that are older than you, and they're still wearing them.