The definition of “hosting” doesn't describe a particular service, but a number of services that offer numerous functions to a domain name. Having a website and e-mails, for example, are two individual services although in the general case they come together, so most people consider them as one single service. The truth is, every single domain name has a number of DNS records called A and MX, which show the server that deals with each particular service - the former is a numeric IP address, which defines where the site for the domain address is loaded from, while the second one is an alphanumeric string, which shows the server that manages the emails for the domain. For example, an A record would be 188.8.131.52 and an MX record can be mx1.domain.com. Every time you open a website 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 forwarded to that company. If you have custom records on their end, the browser request or the email will be forwarded to the correct server. The reasoning behind using separate records is that the two services employ different web protocols and you can have your site hosted by one provider and the e-mails by another.