You can use Smart-saving mode to reduce the brightness, turn on/off push notifications, or change your phone's behavior when it is on standby.
For the push notification toggle, check IM and other apps using push notification to disable internet/data connections when the screen is off (you will not receive notifications), or uncheck it to keep internet and push notifications on.
The Extend Standby option saves battery by reducing the frequency in which an app refreshes when the screen is off. Your phone checks notifications once every few minutes rather than continuously,meanwhile, notification might show up a few minutes later (only when your screen is off). You can choose which apps you'd like to bypass this feature and continue to update in real time by tapping the Extend Standby panel.