The definition of “hosting” doesn't describe one service, but a set of services that offer numerous functions to a domain. Having a site and e-mails, for instance, are two independent services although in the general case they come together, so many people think of them as one single service. In reality, each and every domain name has a couple of DNS records called A and MX, which show the server that handles each particular service - the former is a numeric IP address, which specifies where the website for the domain address is loaded from, while the latter is an alphanumeric string, which shows the server that deals with the emails for the domain address. 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 e-mail, 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 email will then be sent to the correct server. The idea behind using separate records is that the two services work with different web protocols and you may have your site hosted by one provider and the e-mails by another.