Click the folder once. Whatever is inside the folder appears as a list of messages in the main Yahoo! Mail window.
Look along the top of the window and you'll see a tab with the the folder's name on it. If you double-click a message in the folder, the message opens in a new window, with its subject on the tab. See it? The Folder tab is still up there, too.
If you want to compose a message or open another message from another folder, these will open other tabs. The idea is to make it easy to refer back and forth from folders to received messages to messages you're Composing by simply clicking the tabs at the top.
In the old version of Mail, you had to click the "Back" button on your browser (or open other browser windows) to refer to other messages, and there was a good chance you'd lose what you were composing. Not fun!