A backlink is a link from a page on another domain, pointing to a page which is placed on your own website domain. An example would be a link pointing from example.com to brugbart.com.
Now. Backlinks come in many shapes and sizes, but the ones that are thought to be really valuable, are the ones coming from quality sites on a specific topic. One of the factors search engines use to rank pages in the SERPs, is the backlinks pointing to a specific page.