It's good to have a Facebook "Like" button on your website so that people can like your website / web page. What this does is have the fact that they like it appear in their timeline. Their friends see it and this gets more people checking out your website.
Also, Google and other search engines look for what are called "social signals." When your website is liked or bookmarked on social media websites, that means that people are talking about your website or are interested in it. This means your website or content is relevant and this helps your website rank higher in search engine results.
Webstix can help you install Facebook Like buttons on your website. Also, here are some resources which may help you: