Lock phone after / Lock automatically
This setting allows you to set a grace period that applies from the moment your device's screen turns off, during which time the device can be woken up without needing to perform an unlock procedure.
When you wake up your phone after its screen has turned off, normally you will be required to perform the unlock procedure which is configured under Screen lock. This setting allows you to avoid the unlock procedure if the screen has only been off for a short time.
For example, if this is set to 30 seconds, you will not be required to enter your unlocking procedure if your phone's screen has been off for less than 30 seconds.
Some devices also have a Lock instantly with power key setting, which allows you to specify that there should be no such delay if the phone's screen was turned off by pressing the power key.