The definition of “hosting” doesn't describe a particular service, but several services that offer a variety of functions to a domain. Having a site and emails, for example, are two separate services though in the general case they come together, so a lot of people see them as one single service. In fact, every domain has a couple of DNS records called A and MX, which show the server that handles each particular service - the first one is a numeric IP address, which specifies where the website for the domain is loaded from, while the second one is an alphanumeric string, which shows the server that deals with the emails for the domain name. For instance, an A record would be 22.214.171.124 and an MX record would be mx1.domain.com. Whenever you open a site or send an email, the global DNS servers are contacted to check the name servers that a domain has and the traffic/message is first forwarded to that company. If you have custom records on their end, the web browser request or the e-mail will then be sent to the correct server. The idea behind using separate records is that the two services use different web protocols and you can have your site hosted by one company and the emails by another.