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When a laptop is plugged in and turned on, you will notice the adapter may be warm to the touch. A relatively warm power adapter is normal, especially when the laptop is in use while the battery is charging.
However, if the adapter is quite hot, enough that it could hurt your hand after touching it for a few seconds, there could be a serious issue.
The first thing to check is whether or not 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 to the laptop. The adapter may still be at fault, as well.
Also, check the laptop end of the adapter cord for any sign of damage, such as a bent pin or bend/break marks indicating connector stress. If you notice any damage, replace the adapter or have the laptop repaired.
If you notice the adapter is extremely hot, turn off your computer and unplug it from the wall outlet. Once the adapter has cooled off, plug it back in and turn on the laptop. Monitor the temperature of the adapter. If it becomes hot again, take the laptop and power adapter to a computer repair shop and have the technicians check it.