Making a thread fall prevents it from moving to the top of the thread list whenever it's replied to.
When creating a thread, you can automatically have it fall by selecting the icon on the Create Thread page and selecting Enable Falling. Once posted, the thread will already have falling enabled and will not be bumped when replied to.
To enable falling on an existing thread while you're viewing it, click on the Actions dropdown at the top of the thread. Select Moderate, and then select Enable Falling.
To enable falling on multiple threads, visit one of your boards and select the checkbox next to each thread you want to fall. Click on the Actions dropdown, select Moderate, and then select Enable Falling. This will affect every thread you selected.
These same steps can be followed to disable falling on a thread. The menu option to enable falling on the thread will simply be changed to Disable Falling.