Companies that employ overly aggressive techniques can get their client websites banned from the search results. In 2005, the Wall Street Journal reported on a company, Traffic Power, which allegedly used high-risk techniques and failed to disclose those risks to its clients. Wired magazine reported that the same company sued blogger and SEO Aaron Wall for writing about the ban. Google's Matt Cutts later confirmed that Google did in fact ban Traffic Power and some of its clients.
Google uses a hyperlink based algorithm (known as ‘PageRank’) to calculate the popularity and authority of a page, and while Google is far more sophisticated today, this is still a fundamental signal in ranking. SEO can therefore also include activity to help improve the number and quality of ‘inbound links’ to a website, from other websites. This activity has historically been known as ‘link building’, but is really just marketing a brand with an emphasis online, through content or digital PR for example.
You can confer some of your site's reputation to another site when your site links to it. Sometimes users can take advantage of this by adding links to their own site in your comment sections or message boards. Or sometimes you might mention a site in a negative way and don't want to confer any of your reputation upon it. For example, imagine that you're writing a blog post on the topic of comment spamming and you want to call out a site that recently comment spammed your blog. You want to warn others of the site, so you include the link to it in your content; however, you certainly don't want to give the site some of your reputation from your link. This would be a good time to use nofollow.
A backlink is a reference comparable to a citation. The quantity, quality, and relevance of backlinks for a web page are among the factors that search engines like Google evaluate in order to estimate how important the page is. PageRank calculates the score for each web page based on how all the web pages are connected among themselves, and is one of the variables that Google Search uses to determine how high a web page should go in search results. This weighting of backlinks is analogous to citation analysis of books, scholarly papers, and academic journals. A Topical PageRank has been researched and implemented as well, which gives more weight to backlinks coming from the page of a same topic as a target page.