Email hosting is a service in which your email messages and associated files are all stored on a server. When you receive an email to your website’s domain address, the email is routed across the internet and stored on the recipient server. At this point, the server administrators will determine which action to take (reply or ignore) bearing in mind any spam filters, re-routing requests and if the sender is on any blacklists.
The server hosting email can be the same server that’s hosting your website content, a server managed by another host, or two different servers managed by the same hosting company. Email hosting providers might specialize in offering only email hosting services, but it’s more typical for companies to offer bundled emails and web hosting packages these days.