In search engine optimization (SEO), backlinks refer to hyper-links pointing to a particular Web page. Backlinks are important to SEO, because Google considers the quality and quantity of backlinks to determine PageRank.
To be clear, backlinks aren't the single determining factor for search rank, but they are a factor that's often abused for cheap boosts in Google search results. Google is constanly tweaking their search ranking formulas in order to weed out pages that earn their rank through cheap tricks. Overstock.com and JC Penny's ran into trouble for creating an artificial web of backlinks in order to inflate their ranking. (To be absolutely fair, it was likely the marketing firms they hired that did the rogue backlinking, not the companies themselves.)
If you'd like to get backlinks the legitimate way, create great content that people want to link. That's easier said than done in this age of social media, because most social media tools use links that are automatically tagged as "nofollow" for Google in order to prevent spammers from using the system as an automated backlinking system.