Yahoo Mail web by default offers a single message inbox view. So, for reading and replying to messages, you need to switch back and forth to the inbox to open different messages.
There is an option through which you can enable tabbed messages for this inbox.
Here is how:
Login to your Yahoo Mail web version and click the Settings icon from the top right.
From the menu, scroll to the Message tabs section and enable it.
On enabling, the Yahoo Mail inbox will reload and now you can open multiple messages as different tabs.
You can then switch to different tabs to view and reply to messages.
By the way, Gmail offers a more powerful feature of multiple inboxes for better email management.