Hangouts is where you can be in touch with your friends, via voice or videos calls, text messages and so on. To sign out of Hangouts app in Android do as follows:
1. Open Hangouts in your Android device
2. Tap the 3line icon on the top left to open the sidebar menu (or simply swipe to the right)
3. Go to the Settings.
4. Select the account you'd like log it out
5. Scroll down and under the Account settings, tap the Sign Out option
6. Now you are no longer logged in to your Hangouts account in Android