Another example:

A hollowed box with cylinders sticking through it:



With the inner faces selected:



Then boolean union will generate this:



With the outer faces selected:



Then boolean union will generate this instead:




Basically by making a face selection of just the outside it lets you make the booleans temporarily disregard the inner hole. And with a face selection of just the inside part it makes the booleans temporarily consider the outside to be extremely thick. But all just by making a selection.

- Michael