There are usually three classes of hosting, which affect how many people you can sell services to on a single box, and hence the price of the service.
Shared hosting - Single OS, with a single web server, using a single IP address, serving possibly hundreds or thousands of clients on the same box. Lower quality of service since naturally CPU and memory usage is shared, as is the execution environment, which may also affect security or services that can be offered. Also, due to the nature of SSL and HTTPS, you can't have your own private HTTPS domain on such a box. It would need to be shared with everyone else, and hence likely administered outside of your control. Prices are typically around maybe 1$-5$ per month?
Virtual private server - multiple OS on a single box, each client has complete control of their own OS, and has their own IP. Running a web server, or any other service is at the discretion of the client paying for the service. If you're running a web service here, you have complete control over the web server and it's execution environment. CPU, memory, and disk space are shared with other clients on the same physical hardware, usually using a fixed allocation. Sometimes there is a fixed minimum, instead of just a fixed maximum, or no fixed resource usage. Schemes without a fixed maximum are usually referred to as burstable. If say CPU is burstable, then you can potentially use up to the full CPU power of the native hardware if nobody else is using it. Usually CPU is burstable, while memory and disk space are fixed, but not always. If having control of the environment is more important than performance, the box can be over allocated, so the maximum (or reasonable usage if no max is set) of everyone on the box exceeds the physical limitations of the hardware. This can work because some accounts will likely be using less than their full share. In this way, the actual usage (on average) can about approximate the physical hardware's limitations. You can probably get a VPS account for about 6$ on an oversold box, and 15$-20$ for a small slice on a non-oversold box. Prices can go up quite substantially as more hardware is allocated to you.
Dedicated server - you have complete control over an entire machine. You have basically the same control over the environment as a VPS, but the hardware isn't shared, so you have higher hardware capabilities. The cheaper end of dedicated servers that I've seen start around 40$ per month.
