Click a message and it will open the conversation related to the message:
Click a voicemail and it will open the playback window for the message:
So how do you actually delete a message or a voicemail?
Simple, you need to click the icon to the left of the message or voicemail to select it:
You can select several messages or voicemails this way. A Delete button, counting the number of items you selected, will appear at the bottom of the window. Click it and you will be asked to confirm the deletion. Or click the Cancel button next to it to unselect all the items.
Remember that you can display and delete both messages and voicemails at the same time from one screen if you select the All tab.