When you unplug a laptop it should automatically go into a power saving mode in order to extend battery life.
When it is plugged in it will run at full power.
If you run full power with it unplugged and play games or watch movies you will drain the battery much faster.
So if you are playing games, do so with the laptop plugged in if you can. Games should perform better and you wont be limited to how long you can play due to battery life.