Building on a feature rolled out to iOS earlier this year, Facebook is now letting Android developers put Like Buttons in their apps that link directly to a specific page in Facebook. The Like Buttons within apps will work the same way they do on the web and in the Facebook app itself, letting users choose to Like a specific app or page so that they'll see more of it in their Facebook feeds.
Developers have free range to put the Like button anywhere they want in their app, though Facebook promotes the use of it in a few places, such as after completing a level on a game or in the settings of the app. It also recommends that developers revisit their Facebook Pages to make sure they're engaging and ready to accommodate users that come over from the Like Button in their apps. App Links from Facebook can even make it simple for users to move between your native app and Facebook without any trouble.
Source: Facebook Developers