what could be wrong with my laptop?

what you describe definitely sounds like an overheating issue. The main things that you can do yourself would be to make sure the air vents, generally on the side and bottom of the laptop have free and unobstructed airflow. Also you can get yourself a can of compressed air to blow out any dust the may have built up around the fan/heat sink/air vents overtime. However if this does not help resolve the issue then if it's under warranty call the manufacture so they can help you troubleshoot the issue and replace the failing parts which could include the CPU, Heat Sink Fan and motherboard. If it's not under warranty then you are probably going to have to replace your laptop.

You're overheating. The side of the laptop sucks air in and the back vent blows air out. If you're going to help by using a fan, place it at the side of the laptop as to increase airflow. You should first start by cleaning out your vents with compressed air. If you've already experienced it turning off because of your system overheating, it may have already ruined the bearings that allow the fan to spin freely. You may want to check that your fan is blowing at all. Over heating will ruin a system altogether. Don't even turn it on again until you clean it. This is one of the biggest mistakes people make with computers, they have to stay clean.

You answered your own question. Heat, and too much of it. Clean the air intake and exhaust ports with compressed air and a vacuum. Do NOT direct a fan at the rear exhaust port. That does nothing but keep the heat in the laptop that the fan inside there is trying to blow out.

Have you tryed to clean the laptop from dust? Its a good start to blow some air and dust off all from the inside. Dont forget to open the back panel.