Backlinks or inbound links play a big role in the SEO of your webpage. They are links from one website to another.
For example, if you advertise clothes on your website and there is a link on another website advertising clothes that directs to your website, then your website earns a "vote" from Google.
The more so called "votes" you get from Google, the more search engines conclude that your website contains valuable content that deserves to be placed in higher ranking positions.