Back Links are an internet term for inbound links. So a back link to a hub page would be a link from an outside web page to the hub page.
A link out from a hub page would be a back link on the external page.
Why do they matter? One word: Google.
Google sees backlinks as incredibly important. If a page has several backlinks, ideally from different trusted websites, it knows that web page is considered worth linking to and therefore useful.
The text within the backlink matters as well, so if the text page that receives backlink is about "widgets", and the link to that page uses the word "widgets" as the link itself, then Google says "that trusted site not only trusts this webpage, it also believes it is about widgets".