What Are Backlinks?
Backlinks are the links to a website that originate from other websites, which are on other domains. Google algorithmically weighs backlinks to help determine a site's authority. If a site has backlinks from an authoritative source, Google and other search engines will view that site as having more authority, making them crucial for search engine optimization.
As Google puts it, "Backlinks display other webpages that link to your posts." So say for example a few blogs link to an article published on your site. Your site would receive backlinks directing you to the new blogs that cited your article.
The best way to think about backlinks is as though they were roads. Imagine your page is a place somewhere out in cyberspace. If there are no roads -- no links -- to it, how will anyone go to visit it?
The more authoritative the link, the bigger road will be, too, since a more authoritative link will bring in more traffic, just as a road with more lanes would. For example, say you wrote an article on Spinosaurus aegyptiacus -- the largest dinosaur to ever walk the Earth -- and both CNN and a little hobby blog write an article that links back to yours. Since CNN is a more valued, trusted, quality site than the hobby blog, its backlink will be more authoritative.