When a laptop power adapter is plugged in to a laptop and the laptop is turned on, you will notice the adapter may be warm to the touch. The more the laptop gets used, the warmer the adapter may become. A relatively warm power adapter is normal, especially when the laptop is being used and the battery is being charged.
However, if the adapter is quite hot, enough that it could hurt your hand after touching it for just a few seconds, this is a potential problem. An adapter that hot is a warning sign that something could be wrong with the adapter or the laptop.
The first thing to check is whether the laptop battery is gaining any charge with the adapter plugged into an outlet. If it is, then the issue is most likely with the adapter itself. If the battery is not charging, there could be an issue with the power connection in the laptop, as well as the adapter.
Also, check the end of the adapter cord that connects to the laptop, as well as the power connection on the laptop, for any possible damage. This damage may include a bent pin inside the connector or bend/break marks in the metal jacket of the connector. If you notice any damage, replace the adapter or have the laptop repaired.
If you notice the adapter is very hot, unplug the power adapter from the wall outlet. Let it cool down completely, then plug it back in to the wall outlet and turn on the laptop. Monitor the temperature of the adapter for a while and if it becomes hot again, take the laptop and power adapter to a computer repair shop and have them check it. An issue like this is not something you want to ignore, as it could cause serious damage to a laptop or even potentially start a fire.