Let's say you have a website named A. If another site named B links to your site A, the link on B is called a backlink to A.
From wikipedia:
Backlinks are incoming links to a website or web page. Inbound links were originally important (prior to the emergence of search engines) as a primary means of web navigation; today their significance lies in search engine optimization (SEO).
Why are backlinks important?
The search engines base their rankings on several factors, the biggest factor being how many backlinks are connected to your site. The more backlinks, the better.
How do you set up a backlink?
The two most popular ways are:
1. Find popular forums that relate to your niche. In each forum register and begin responding to some conversations. In all forums there is a Control Panel where you can edit your profile and put in a photo or avatar. Fill that out and leave the signature blank for a while. Return to the forum for at least a week establishing yourself as a genuine member. Then go back into your profile and add your signature. This signature will be at the bottom of everything you post on that forum. Make sure you include a link to your website in your signature. This is your backlink.
2. Another popular way is to write an article and post it in an article index website such as EzineArticles.com. Do your best to use good spelling and grammer; aim for high quality. This time you will include your website in the Author's Resource Box, which is similar to your signature in the forums. The more articles you write the better. There are many resources you can use to help you write. Ezine Articles has some videos and some other helps to get you started.