To delete multiple messages from Thunderbird mail, select the small box symbol to the right of "Total" on the "Subject" line of the mailbox for any folder. Click on the "Select Messages" entry at the top of the list of options. That will add the selection boxes to the left of all messages in the folder as well as a box at the top of these boxes to select all boxes. Then you can delete, move, and take other available actions for the checked messages---just like with other mail clients.

(Please post this help note to the archived question that is answered above since the archived answer does not address the best use of Thunderbird Mail's capabilities.)