Deleting a thread will remove it from your forum entirely. Remember that once a thread is deleted, you are not able to un-delete it!
To delete a thread while you're viewing it, click on the Actions dropdown at the top of the thread. Select Moderate, and then select Delete.
To delete threads while viewing the list of threads in the board you're currently browsing, select the checkbox next to each thread you want to delete. Click on the Actions dropdown, select Moderate, and then select Delete. This will delete every thread you selected.
To select specific posts to delete from a thread, click on the button next to a post while viewing a thread, then select the Select Post option from the menu. Click on the button again and hover over the Moderate option, then select Delete Post from the sub-menu.
You'll be prompted to confirm you want to delete the threads before they're removed. To confirm you want to delete the threads, select the Delete Thread(s) (or Delete Post(s)) button.