"Page Subtree Activation Check" was introduced to control the behaviour of page deletion. This option needs to be enabled if the subtree of the page under consideration is to be checked for any activated descendants before performing page operation such as delete. By default, this option disabled.
For page deletion, if this option is disabled, then, since we cannot know the activation status of the descendants of the page, therefore, the page cannot be deleted directly because of the risk of deleting any activated descendant also. On the other hand, on enabling this option, the descendants of the page will also be checked for their activation status. And, if it is found that no page in the entire subtree is activated, then the given page will be deleted since direct deletion would be safe now.