The definition of “hosting” doesn't describe a particular service, but a variety of services which provide numerous functions to a domain name. Having a site and e-mails, for example, are two separate services even though in the general case they come together, so most people consider them as one single service. Actually, each domain has a number of DNS records called A and MX, which show the server that deals with each specific service - the first one is a numeric IP address, that identifies where the site 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 can be 18.104.22.168 and an MX record is mx1.domain.com. Whenever you open a website 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 directed 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 reasoning behind employing separate records is that the two services work with different web protocols and you can have your website hosted by one service provider and the emails by another.