SEO, Backlinks???

In Short: Backlinks are links to your website from another website.

However, it's much more complicated than that. You want backlinks on sites with a high PageRank that are do-follow backlinks. Let's look at some examples:

No-Follow Backlinks: I update a wikipedia article with a link to my (relevant) website. Wikipedia, as one would imagine, has a very high PageRank. However, the links on wikipedia are no-follow links. This means that when Google crawls the page, it will not count the links as backlinks to your page. This is done to prevent people from spamming wikipedia and other sites with links as it won't help them rank on google. There are tools you can obtain for Chrome that will show whether or not a link is do-follow or no-follow.

Do-Follow Backlinks: I have a friend who runs a popular blog. He let's me do a guest post and I add a link to my site. Google will crawl his site, see my link, and know that my site is important because it's linked on this high PageRank site. This will improve my SEO and ideally other people will see this and do backlinking for me by blogging about my site or linking it from their sites.

Hope this helps. I'm still a bit of a SEO noob, but this is my interpretation after much research.