Think of links as votes for your page! Search engines are just computers, they might be great at reading and indexing pages but they don’t actually understand them (not yet anyway!!!)
In order to decide on the quality of a page, search engines look at what other sites link to it. For example, if page A links to page B, and Google already ranks page A as an authority on a subject, it will count that link as a vote for B and award it a little extra authority too!
Two important things to remember when it comes to links. Firstly, not all links are equal. A single link from a well ranking authority site is much more powerful than many links from sites which don’t hold as much weight with the search engines. Secondly, the anchor text of the link is important. For example, a link such as: Click to learn web design with the words “web design” as anchor text, is much more valuable than with “click here” as the clickable link.
The reason being that the anchor text in the first example is relevant, and will help the page being linked to rank better for that term, while the second is not descriptive (unless you are trying to rank for the key term ‘click here’!)
Now as I said before, there really is an awful lot more to be said on the subject of SEO, but if you concentrate on backlinks with proper anchor text you’ll already be streets ahead of the competition.