Backlinks simply work using the same principle of referring and recommending other businesses offline to a prospective customer(s).
For example, people tend to buy easily without hesitation from a business they do not even know or met before as long as the business was recommended by their trusted friends, family, co-workers and others. But, do hesitate if the business had come to them directly for the first time.
A backlink is other people (websites) recommending you (your website) to Search engines like Google. Though without their recommendations, the crawlers might still end up crawling but when you have more website recommending you, Google and others see your website as providing quality and helpful content and thus compensate you with a higher ranking in search results.