Backlinks (sometimes called ‘ inlinks’ , ‘ inbound links’ or “links to your site”) are hyperlinks on other people’s websites that link to your website. You might also hear the term “referring domain”. 100 links from the same website = 100 backlinks but only 1 referring domain.
Why do we look at them?
In very simplistic terms, search engines look at the number, but more importantly the quality of links pointing at your website as an indicator of how respected, trusted and useful your website is.
To ensure that this remains a useful metric for the search engine to rank their results, Google and their contemporaries have been known to crack down hard on websites that have clearly manufactured spammy links to try and game the system. It's a great idea to monitor your backlinks to check for this kind of thing. Noticing unusual spikes in backlinks and referring domains has allowed us to spot all kinds of odd new problems.