When you register your app, you can get detailed analytics about the demographics of your users and how users are sharing from your application with Insights.
The Graph API provides programmatic access to all of this data so you can integrate Platform data into your own, custom analytics systems.
To download Insights data, you first need to obtain an app access token. You can learn more about what makes an app access token different than a user access token in the login documentation.
Once you have your application access token, you can download analytics data for your application at:
https://graph.facebook.com/app_id/insights?access_token=...
That URL outputs all of the analytics data available via the API, including the total number of users, number of active users, and a number of other detailed metrics. For example, you can get the number of impressions of your app's canvas page:
https://graph.facebook.com/app_id/insights/application_canvas_views/day?access_token=...
You can use since and until to specify the time range for which you want data. Both arguments accept times in almost any valid date format:
https://graph.facebook.com/app_id/insights?access_token=...&since=yesterday
Explore the Insights product, the base /insights URL, and the Insights documentation for more information.