Having back links means you are getting votes for your web pages. Other web pages are saying that your web page is a good place to find "WhateverYourPageIsAbout". Back links also provide access for search engines to find your content and index it.  

In addition to giving search engines access and giving your web pages votes, back links tell search engines what they'll find on your website based on the "anchor text" or the words which are hyperlinked to go to your site..

If thousands of people are saying something is good and then you go and check it out, and it is good, you'll probably start telling people it's good as well. Back links tell search engines and then  search engines start referring you. 

It is believed that Google likes your site being linked to from different class ‘c’ websites.

The more links from different class 'C' websites the better! Try and get as many as possible.

The first place is to use to get back links is to look through free resources. There are many great resources out there and here is a good place to start. A company in Canada called SEOcompany.ca. 

http://www.seocompany.ca/directory/free-directories.html

This is a time consuming process but it's worth it.  You can get someone to do this for you for a small fee from many forums and other resources. I would not submit to submition services but get someone to submit to the free directories

Some of the resources listed in this seocompany.ca list are not free, some are cheap and some are expensive. I feel there are a few, if you can afford it, that are worth paying for as well.

Don't forget the main search engines as well, http://dmoz.com which I feel is the best is free, however, it takes a long time to get listed.