AWS is a modular, pay-as-you-go system. This is why they have so many different prices for different things. It's broken down into as small of a unit as possible so you only pay for what you use. This is in stark contrast to purchasing your own server where you have tons of fixed costs regardless of your scale or traffic.

But there are a lot of hidden costs that you don't realize with buying and managing your own servers. You have to deal with cooling the unit, power failures, backup generators, physical and digital security, hardware failures, hardware upgrades. And when you want to expand beyond what one physical server can handle, now you need to go buy and setup new hardware. This is a slow process and you cannot react very quickly if a spike in traffic occurs overnight.

So you need to take time to analyze your use case and what you need and calculate all of the costs. But you'll usually find it's cheaper if you plan it out right.