Backlinks are links from other sites to yours, and search engines read good ones as credibility votes. They remain a real ranking force. With all the emphasis on 'good': ten links from real local organizations beat a thousand from link farms.
Buying them: no. Paid link schemes violate Google's policies, penalties still happen, and the links $200 buys are precisely the ones worth nothing. The 'safe paid links' pitch has separated small businesses from money for fifteen years.
How local businesses actually earn links without a campaign: chamber and association memberships, suppliers' dealer pages, local news when you do something noteworthy, sponsorships with a linked mention, and being the cited answer (which is what a resource hub is for).