Archive emails in Mail on Mac
If you don’t have time to read or take action on an email message when you receive it, you can archive it. Archived messages are stored in an Archive mailbox so you can quickly find them later.
Archive messages you receive
On your Mac, do any of the following:
When a Mail notification appears in the top-right corner of your screen, move the pointer over the notification, then click Archive.
If Archive isn’t an option in the notification, set the “Move discarded messages” option to Archive in Viewing settings in Mail.
In the Mail app
on your Mac, select one or more messages, then click the Archive button 
in the Mail toolbar (or use the Touch Bar).If you select an email conversation, any message in the conversation that’s in the current mailbox—for example, the Inbox—is archived; related messages that are in other mailboxes aren’t archived.
View archived messages
When you archive a message, an Archive mailbox is created for the related email account and the message is moved there.
In the Mail app
on your Mac, in the Mail sidebar, click the Archive mailbox for an account.