The definition of “hosting” doesn't describe a particular service, but several services that offer different functions to a domain address. Having a website and emails, for instance, are two separate services even though in the general case they come together, so many people consider them as one single service. In fact, every single domain name has a couple 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 website for the domain address is loaded from, while the latter is an alphanumeric string, which shows the server that manages the e-mails for the domain. As an illustration, an A record is 188.8.131.52 and an MX record would be mx1.domain.com. Every time you open a website or send an e-mail, 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. In case you have custom records on their end, the browser request or the email will then be sent to the correct server. The concept behind using separate records is that the two services employ different web protocols and you could have your website hosted by one company and the emails by another.