When you register your domain with a registrar most of the time the company you go through will offer to host your website for an added cost. Furthermore, when you go through any hosting company what you are signing up for is a managed hosting service. What this means is that the company you have gone through is managing all of the different things required to get your website up and running and to keep it that way. The hardware, software, upgrades, backups are all part of the services you pay for.
In a shared hosting scenario many customers are all sharing the resources of a single server. A server used for this scenario is designed and set up to operate efficiently in this way, allowing customers and visitors to access it all at the same time.
In another scenario a person or organization might require a virtual private server. Sometimes people refer to this kind of situation as a dedicated hosting account, or a dedicated server. In shared hosting and in dedicated hosting the provider is responsible for starting and maintaining the hardware and software systems that are necessary. Backups, technical issues and maintenance are all taken care of by the host provider. Regardless, in this case the entire server is dedicated to just the one customer.
In situations where a host provides a dedicated server service the customer often has an added level of control over the server. They can run multiple websites from the server if they so choose, and can control ways that the server functions.
Still there are more options such as virtual dedicated and reseller shared hosting which can meet some customers needs half way. Still maintained like the others but varying levels of access, cost and kinds of use.
Finally, we get to colocation.
Colocation is when you purchase and own the server and your own software that will serve as your host. You will completely configure and operate this hardware for yourself. You will install the system in the same data center as the providers and the provider will offer some assistance. The provider is giving you space in their cabinet to place your hardware and they will provide you with power, access, and IP addresses. In this situation the provider will offer varying levels of support.