Backlinks (incoming links) refer to all links on other websites that refer to the website in question. Search engines are geared towards sorting search results according to the concept of real life recommendations. The better you are the more recommendations you receive. Search engines interpret a link to a website (backlink) as a recommendation for it.
The more backlinks a website has and the better those links are, the further up it will appear in the search results. An example of strong backlinks would be links from topically relevant websites.