Links to your website from other websites, called 'backlinks', are a key part of how Google measures the authority of your website and the nature of the content on your website.
A backlink is like a vote of confidence from another website. Links from websites with high domain authority (DA) count for more than links from websites with low domain authority.
Most SEO experts agree that backlinks are one of the top three factors determining how a website ranks in the search results. Backlinks are so important that many website owners spend more time building links than creating new content.
Link building is a huge area within SEO and there are dozens of different link-building techniques that people have discovered or developed over the years. Some of these techniques are acceptable to the search engines (so-called 'white hat' link building), while others are frowned upon ('black hat' link building).
In general, black hat link building is where a website owner acquires a backlink not because the content was outstanding and valuable, but because they entered into some kind of link exchange arrangement with another website owner.
These link schemes are expressly forbidden in Google's Webmaster Guidelines.
Here are some useful articles on building backlinks:
By Rob Powell