What are backlinks?
Backlinks are like breadcrumbs. Tasty little morsels scattered about that will lead people to your content. You can create great content, whether it be articles, images, video etc, but if there are no links pointing to your media it will be an uphill struggle getting it found. Basically backlinks are links to your page(s) from other domains.
Why build backlinks?
Backlinks are about getting your stuff noticed; by people and search engines, so its value can shine through. A lot of web traffic is generated through surfers using search engines. To get any sort of presence on search engine results you need backlinks as the search engines use them to determine the value of your webiste, blog, article or manifesto for world domination. You could be the World's next best thing and solution to Climate Change, but it aint gonna happen without backlinks baby!
The more high profile, trusted, relevant and busy sites are the more valuable the backlink from it will be. In an ideal world you'd create your content and let these links develop naturally. The trouble is if you do that it is more than likely they'll never appear, or you'll be waiting a long time at best. Just like Grandma said, "If you want something done, better go make a start yourself ..."
How do you build backlinks quickly?
In short you find places on the web that have some form of user interactivity so that you can create content on that site that includes a link back to your own site. With web 2.0 this has become a lot more common and so isn't too hard. Blogs, forums and social networking sites are all obvious potentially valuable places to create backlinks. The more popular the site in terms of traffic the better, however relevancy to your content is also extremely, perhaps even more, important.
The trick now is in understanding where to target your efforts and how to do it constructively. This will vary depending on your content and market but there are some general rules worth considering. For instance placing comments on popular blogs is a quick way to create links back to your own blog or content. However it is important your comment contributes something worthwhile to the discussion and isn't simply spam.