Facebook Insights is a tool that allows you to track how many people visit your page, how many people like your page, how many people see individual posts and how many people are interacting/engaging with those posts.
Here is a “cheat sheet” of what each category can tell you:
Overview: Facebook provides a summary of recent activity on your page from last seven days (default).
Page Likes: Total page likes you have; Positive or negative growth over the week.
Post Reach: Number of people who saw posts via organic (found by themselves) or paid (paid to promote page or post); Compares reach in the last week to the week prior; When people like, comment or share your page, you reach more people; When people hide, report spam or unlike your page you reach less people.
Page Visits: Number of times each of your page tabs was viewed; Page tabs are located at the top of your page’s timeline, under the cover image, including About, Photos, Events, etc.
Other Page Activity: Number of actions people took involving your page, such as mentioning it, posting on your page, checking into your page, or purchasing an offer from you.
External Referrers: Any website linking to your Facebook page that people arrived from.
Engagement: Measures likes, comments, shares and clicks on your page posts
Recent Posts: By default, this shows details about your five most recent posts
Post Types: Shows the success of different post types (photo, status, link, video) based on average reach and engagement
People: Shows the demographics of Your Fans, the People Reached, and the People Engaged so that you can better develop and target your content.