The definition of “hosting” doesn't describe a particular service, but a number of services that provide numerous functions to a domain name. Having a website and e-mails, as an example, are two separate services although in the general case they come together, so most of the people consider them as one single service. In fact, each and every domain name has a number of DNS records called A and MX, which show the server that manages each specific service - the former is a numeric IP address, which identifies where the site for the domain name is loaded from, while the latter is an alphanumeric string, which shows the server that manages the emails for the domain name. As an example, an A record would be 126.96.36.199 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 name has and the traffic/message is first directed to that company. In case you have custom records on their end, the web browser request or the e-mail will be forwarded to the correct server. The reasoning behind employing separate records is that the two services employ different web protocols and you could have your website hosted by one company and the e-mail messages by another.