Backlinks are very important for SEO as Google use them to calculate web-site PageRank (PR). Each backlink is counted as a vote!
Now you don't have to be a rocket scientist to understand that more backlinks means higher PR and higher rankings. Many knowing that get involved in what is knows and "link exchanges scheme". Basically they start exchanging backlinks with other sites in return for including links from other sites on their own website.
One-way backlinks are the ones Google likes. This means that the website is linking to other site without the reciprocal link.
Many recur to black hat SEO and start doting what's known as two-ways backlinks. You link to my site and I link to yours. These practices are considered bad for SEO and could result in penalty.
Please read this post to understand what is: one-way-two-way-three-way-linking