Amazon EC2 is a typical IaaS. This service lets users lean using simple API calls, servers to deploy applications, storage, or network routers. It only gives you the hardware, which you then have to manage to get your whole technical stack up and running. You have to select (or build) a virtual machine image (such as AMI) with your preferred operating system, configure network and routing, attach disks for persistent data, and so on. It looks like going to your favorite broker to buy PC components and build your own computer. The main benefit is that you only pay for what you actually use, so you can change your mind and get a bigger or smaller server, or just drop everything at anytime.
IaaS was a required, but low-level step in Cloud revolution. The flexibility it gives you is huge as compared to the bare-metal hardware, even with existing rent options. You can get dozens of servers available in few clicks, with ridiculous cost that only relates to the duration for which you actually use them.
The main drawback is that you only get the hardware. Operating system setup, low-level configuration, middleware installation, security, monitoring, and maintenance are your responsibilities. This makes sense if you have some very specialized software that you want to run, but for common technical stacks that are the concerned standards, this doesn't make much sense. If you need your own patched version of Linux kernel, IaaS is for you. If you want to run a Java application under the latest version of Tomcat, you will end up spending hours of engineering time just to set up and maintain the basic runtime that your developers are expecting.