in a nutshell, backlinks are the internet equivalent of word-of-mouth recommendations. that is, a backlink essentially tells google that the website receiving the backlink is worthy of a higher rating.
just like you would listen to your friends when they tell you to try a new restaurant, google "listens" to the web by counting a websites backlinks. the more people who suggest you try the restaurant, the more credibility you will give to that establishment.
furthermore, there are situations when 1 backlink is more powerful than 10 backlinks. this is the equivalent to your 1 best friend telling you that you MUST try this restaurant verses 10 random people telling you that you must try it.
this is how backlinks work theoritically. but practically speaking, a backlink is a hyperlink on another person's website that will direct the website visitor to your website. usually, you want the hyperlink to point the visitor to an important page of your website and you want the text that the visitor reads (called the anchor text) to be something relevant. for example, an anchor text like Click Here! is not as powerful of a backlink as "Get Rich Quick by Clicking Here"
good explanation?