Vestibules. Originally conceived as an air lock to keep gusts of cold winter air from entering the home, the vestibule has taken on a character all its own. Not quite inside nor outside, a vestibule is meant to be a transitional space that keeps rain, mud and unwanted guests out of the house proper. These transitional spaces, though more common on older homes, can find their way into a more contemporary aesthetic, as can be seen here.
They're worth having If you live in a cold climate and you use it as an airlock - keeping the inner door closed unless you're entering or exiting.
If you're going to leave the door open all the time as it is here - then the added expense is pointless.