Deleting a message is permanent, whereas when you archive a message, it's still available; you just won't see it in your ...

Click the Archive icon, which looks like a box with a down arrow, and appears to the right of the email's sender information and description. Once archived, the message will move out of your inbox.

Access an archived message by searching for it or by going through the All Mail inbox. If you're on the web, click the Move to Inbox icon on the top dashboard. It's to the left of the Label icon.