Google Mail stores ALL of your messages in one big container called Archive. Then, labels are applied to some of those messages to make them visible for you. Some labels are created by the system and are hidden. These labels include Inbox, Sent Mail, and Drafts. You see messages in your Inbox, because the system applies the label "Inbox" to them. Other labels are created by you and show in a list down the left sidebar of the Google Mail window. When you apply a label to a message or move a message to a label, what actually happens is that the message remains in your Archive but is visible based on the label. Messages in your Inbox that you move to user-created labels have the Inbox label removed and the user-created label applied. In addition, unlike folders, you can apply multiple labels to a message.
Going the other direction, when you select a message and click the Archive button, you are removing any applied labels. The message is now just another message hanging out in your Archive. To find a message in your Archive, use the Search Mail field at the top of the Google Mail window. You can also, scroll to the bottom of your labels, click the "more " link and select All Mail.
One of the Google Mail Labs creates a 'Send and Archive' button which does just that - sending and archiving at the same time when you forward or reply to a message. While you could send, then select the original message, and finally click Archive, the 'Send and Archive' button is a faster way of doing this.
To enable the 'Send and Archive' button, click on the gear in the upper right of the Google Mail window, select Mail Settings, and click on the Labs link. Scroll down through the Labs (alpha order) to locate Send and Archive. You can also enter "archive" in the Labs search field to show the Send and Archive. Click the Enable radio button. Finally, at the top or bottom of the window, click the Save Changes button. Send and Archive will be enabled and you'll be returned to Google Mail.
When forwarding or replying, after clicking Send and Archive, the message will disappear from your Inbox or label. Don't worry, if a message recipient replies, the entire message conversation will reappear in your Inbox. You can also use the Search Mail field at the top of the Google Mail window to find the message.