Why?  Because search engines place a lot of weight on how many links you have coming to your site from other sites.  These are called backward links.  So, here is a simple example.

You sell widgets.  I sell widgets.  You have 100 sites linking to your site saying that your sell widgets.  I have 10 sites linking to me saying that I sell widgets. 

Someone goes to a search engine, and types in 'widgets'.  Your site would rank above mine since you have more links from other sites pointing to you.

It's a bit more complicated than that, but you get the idea.  Other factors include the number of links that the web sites pointing to you also have.  So now comes the interesting part.  There are 3 ways to link, the Good, the Bad, the Ugly.

The Good

Finding link partners in your area of expertise.  For example, if you sell widgets, a link from a site discussing the benefits of widgets is far more valuable than a site that discusses gardening.  Your visitors, and their visitors will likely find more information on widgets far more useful than a link to a random, non-related web site.  Many link exchange sites offer you the ability to find link partners by category.

The Bad

If you're not careful, you can wind up exchanging links with "bad neighborhood" websites.  Know your link partners, look at their websites.  Avoid link farms and sites that don't offer value to your visitors.  Don't blindly exchange links.

The Ugly

Too many links, too fast.  Don't sign up for services that suddenly get you 1000's of links in a day or 2.  This won't help you.  Too many links too fast is a red flag to search engines, and they'll ignore the links.