The definition of “hosting” does not describe one service, but a set of services that offer different functions to a domain. Having a website and emails, as an illustration, are two separate services despite the fact that in the general case they come together, so many people think of them as one single service. In reality, every domain name has a number of DNS records called A and MX, which show the server that deals with each particular service - the first one is a numeric IP address, that specifies where the website for the domain is loaded from, while the latter is an alphanumeric string, which shows the server that deals with the emails for the domain. For instance, an A record is 22.214.171.124 and an MX record would be mx1.domain.com. Each time you open a site or send an email, the global DNS servers are contacted to check the name servers that a domain name has and the traffic/message is first directed to that company. If you have custom records on their end, the browser request or the e-mail will be sent to the correct server. The idea behind using separate records is that the two services work with different web protocols and you can have your site hosted by one company and the emails by another.