When a message is archived in Gmail, it is hidden from the inbox list; however, the email is kept in the account and can be accessed in the future if need be. Archiving simply takes the email and places it in a folder where it continues to exist without cluttering the inbox.
To archive an email, simple select the message by clicking the check box next to it. Then click the "Archive" button on the toolbar above the inbox list. When a message is deleted and not archived, it is sent to a trash folder where it stays for 30 days before it is automatically deleted from the account for good.