You can move messages out of your inbox but still store them for later in All Mail by using the Archive function.

To archive messages:

1. Select a message(es) by checking the box(es) next to the sender's name.
   
2. Click Archive at the top of your inbox, or use the 'y' key if you have keyboard shortcuts enabled.

If you have a conversation or email message opened, you can archive it by clicking the Archive button at the top of the page, or by using the 'y' key if you have keyboard shortcuts enabled.

If you archived a message but now want it to appear again in your inbox view you either search for the message or browse all your messages. To browse all your mail, follow these steps:

1. Click All Mail (If you do not see it on the left side of your Apps mail page, then it is in the 'X more' labels menu)
   
   
2. From the list of messages, check the box next to the sender's name. You can also follow this step if you performed a search for the message you wished to recover.
   
3. Click the Move to Inbox button.
   
   
   
   

1. Click the Move to Inbox button at the top of the message