You can hide content from users (with Advanced Permissions enabled) by not allowing them to view a specific area. Just select the block area in Edit mode and click on Set Permissions. Uncheck the box that allows them (the user/group) to "Read" that area. You may need to Manually Add them to the list.

However, if a block function is enabled, for example you've installed a music player block for your site, my understanding is that anyone who can edit the site or a page can insert it (and thus see the added block). The Advanced Permissions control where they're allowed to insert it and if they can see the area or not. Someone else please correct me if I'm wrong?