Why are backlinks so important?

A backlink is when a site links to you and you do not link to them.  So it is an external or inbound link to your site that is not reciprocated. 

There are three factors that dictate the quality of the backlink:

Anchor text

If you look at these two links, the anchor text is the text that is used for the link. The anchor text contributes to the “authority” of the linked site, meaning what the site is about.  Look at:
osCommerce is the best eCommerce solution.
versus
osCommerce is the best eCommerce solution.
 The first link says the site is about osCommerce which does not say much.  The second is saying it is the best eCommerce solution.  Get the point?

Context

A link that is embedded in prose, as in the middle of a block of text, is considered better than a link that resides in a series of links e.g. a directory page. Why? Because it is seen having more import, sitting there all by itself.   It is less likely to be a contrived link. So the above links are good once for osCommerce.

Page Rank

A link from a high ranking page is seen as having more importance than a link from a lesser ranking page.  So a link from a PR6 page is going to be given more credence than a link from a PR2 page. So this link to osCommerce is not particularly useful to them in that respect.

Monitoring Links

How can you see what links you have? link:www.yourdomain.com will tell you how many links there are to your domain. 
Yahoo and Google treat this command differently.  A search using Google will show links per domain and Yahoo will show links per page thereby reporting a lot more.  To explain, a link in a site footer will put the link on every page.  Google will count this as one link. Yahoo will count every page.  (MSN Live does not recognize this search command.)
Google Webmaster Tools will also give you this information under the  Links > Pages with External Links function.   That function matches the Yahoo results.
When looking for your keywords, the following Google searches are useful:

• allinanchor: keyword phrase will tell you the links that the keyword phrase you are interested in. 
• allintitle: keyword phrase will tell you the links that have the keyword in the page Title. It only works for one word.
• allintext: keyword phrase will tell you the links that have the keywords in the page Text. ignoring page elements like Title and links.

You can limit the above three commands to look just at your site by site:www.yourdomain.com. Google Webmaster Tools will also give you think information under the Statistics > What GoogleBot Sees > In External Links to your site.

Perferred Domain

Note the use of “www” in a link.  Linking to yourdomain.com and www.yourdomain.com is not the same thing. To make it the same thing, you need to set your preferred domain with Google and other search engines to make sure that all links go to your preferred domain. 

How to write a good link?

It’s not solely about SEO.  Customers have to read them too and be induced to click on them.  Jakob Neilson’s recent research on link text indicates the the first 11 characters are the most important.  So you need to carefully craft your text if you want click thru as as well as a backlink.