Why are backlinks so important in SEO?

Back links show that your post/page is important
Back links get more traffics to a page/post
Back links help page/post to be discovered faster
Back links are vote of confidence
And so many more. All these benefits make search engine to value the post/page and rank it higher than ones that don't have bank links, other things being equal.

From the perspective of SEO, there is a difference between backlinks and quality backlinks.

1. For Google search, random backlinks do not offer any help. Google assesses the quality of the backlinks present on a webpage with the relevancy found in the content of both the web pages.

2. The higher is the relevance between the original content and backlink content, the greater becomes the quality of the backlinks.

3. Quality backlinks bring more referral traffic to a website/blog, and most importantly will improve the ranking of a webpage.

Important things to take away:

There must be quality content in place.
Don't create back links if not relevant to either of the site/page.
Back links must be natural, at least look natural to be counted.
No link for linking sake.

Backlink is important in SEO because it is one of the 200+ factors Google considers before ranking landing pages in its SERP.