Email servers, also called Mail Transfer Agents (MTAs), today do much of the heavy lifting required to transport email from sender to recipient, ideally without the sender or recipient being particularly aware of them. They store (queue) incoming email, then forward it to user's mailboxes, sometimes via other email servers, while often trying to avoid accepting or sending out spam or viruses. They also allow users to read email waiting for them in their mailboxes.
Nothing gets "Shut Down". You can't power on VMs, use vmotion, or DRS.