Backlinks are important for sure, in that they're quite impactful. But it's important to get high-quality backlinks, i.e. from websites with high domain authority. Every backlink is interpreted as a 'vote of confidence by the search engine, and the more trustworthy backlinks it finds, the higher score it gives to your domain.
By backlinks, do you mean when websites link to yours?
Well, one of the insights Larry Page and Sergey Brin had was about scientific papers. They found that the more citations a scientific paper had, the more valuable it was.
They took that same insight and put it on Google. They found the best sites had other sites linking to them. So I'd say they are pretty important.
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