Ever since we coined this term on "Mysterium Pictorum" when discussing "A Ghost Story", it doesn't leave my head - Since it encapsulates to well what I would like to do myself.
We've been using the term liberally in the past couple of weeks. Bergman's "After the Rehearsal" was counted into the category by us, as was Svankmajer's "Alice".
What it means is: A movie that tells an intimately small story with which it is talking about universal, big topics (mostly death, if one looks at the examples, but there's limitless potential).
Few characters (often just two or three), few locations (often just one) and, on the surface, not always much going on (thought sometimes a lot is going on on every level!).
Now, recently, the horror genre in general has made a huge shift in the direction of small, intimate settings in one location and with very few characters. Some of them are intimate universalism. But "Paranormal Activity", for example, isn't, even though it superficially might fit the bill.
So, what is it that differentiates "intimate universalism" from these films? I'd say a certain level of philosophizing. Intimate universalism is wondering at things. Either the characters or the films themselves think about the big topics they're about.
I'd love suggestions to expand that list!