In order to help keep your inbox clear and uncluttered, you can mark completed items as "Done" within the Inbox.
There are two ways to mark something as done: either from the card preview in the central pane (in "My Inbox" or any of "My Teams") or from the bottom right corner of the selected conversation.
When you mark something as Done this does not delete the item. You can go back and find this in the "Done" folder. You can find the Done folder by opening the inbox from the inbox icon on the toolbar, and then clicking on "My Teams" from the left-hand pane.
If you re-open a conversation from the "Done" folder, it will go back to the folder it was last assigned to (i.e. where it was marked as done from). However, you can always find this is the "All" folder