What type of server handles the relaying of email messages?

The type of server that handles the relaying of email messages is referred to as a mail transfer agent (MTA). This server is responsible for accepting, forwarding, and delivering email messages between different mail servers over the Internet. When an email is sent, the MTA processes the sending of the message to the recipient's mail server, ensuring proper routing and handling of the message.

The term "mail relay server" typically describes a functionality of the MTA, as it relates to servers that forward emails. However, the most accurate and widely accepted term in the context of managing the entire email delivery process is the mail transfer agent.

Other types of servers mentioned serve specific roles: a webmail server provides access to email accounts through a web interface; a local email server deals with email within a localized network; none of these primarily handle the relaying function in the way the mail transfer agent does. Thus, understanding the role of a mail transfer agent is crucial in the context of how emails are relayed from one user to another.