Why does time slow down as one approaches the speed of light?

At school I am having this debate with my friend, who isn’t sure that time would slow down from the perspective of an outside observer if they were to apporach the speed of light.

I say that it would and use the twin parodox as an example, but I don’t really know why.

The best explaination I’ve heard is that there is a limited ammount of energy one can use to either go through space or time and that the more energy one uses to travel through space the less is used to go through time.

Could someone dumb this whole special relativity nonsence down for me a bit and hopefully resolve this argument so that no one gets hurt?