Have you ever wondered why so many large chain stores have two sets of doors? No, it is not just to store shopping carts.
Where I live, any home that is around 100 years old (that hasn't seen any renovations) will very likely have two front doors. Putting it simply, you open one door, step into a small space, and there will be another door in front of you.
(Image Sources: Image 1 | Image 2)
The space goes by many names, including: arctic entry, mud room, breeze room, vestibule, airlock, foyer, and more. For sake of simplicity, I am going to call them "entry vestibules."
Entry vestibules create a buffer between the outside and the inside of the building, preventing drafts. This can help greatly with temperature regulation in both the winter cold and summer heat. I can't find number details on energy saving, but the fact that large chains still build them may hint of their importance for money-saving.
In homes, this space also typically serves as the mud room ( a place for shoes and jackets).
In the name of "first impressions," and open concept designs, vestibules are often the first thing to go during renovations, and I think that's a real shame.
It's blocks airflow when only one door is open. A cache of sorts. Insulation isn't really the issue, since a single door allows free airflow, regardless of how well insulated the door is.
It's also part of why revolving doors are useful (though those also help with stack pressure in multi-story buildings).
It does two things: 1) a cache when one door is open, 2) and prevents drafts (from improper sealing around the door) like OP said. Insulation of the door is another component of the second part.