a link from any other website, page, or directory, to your website
A link from any other website in the index, to the website in question (your website).
Links from other websites are one of the most important signals to The Algorithm of the relevance of your website. It's most helpful if the pages linking to your site have content and use keywords which are relevant to the topic of your page or website.
The Algorithm values backlinks so highly, however, that there's an entire, highly profitible, industry in creating fake websites (known as "link farms") or spamming links in the open comment sections of Chinese, Russian, and Martian porn sites.
Don't buy links back to your site. You might get a little bump in traffic, but it's unlikely to result in more business and it's potentially embarrassing.