"Up there" and "down there" are two of the most frequent expressions that I, myself, use often. I really don't know whether they are just expressions used to refer to a place to go ("I went down there and picked up the mail") or whether they have some significance attached to them. Like recently at the airport, somebody told me "to go down there for the International terminal" and I wondered whether they meant "down" literally, or was it just the expression?
Prepositions are often interchangeable in English, even when they seem to mean exactly the opposite thing in their literal sense. It is possible, for example, to say
You'll find a Chevron station down the road about five miles.
You'll find a Chevron station up the road about five miles.
You'll find a Chevron station along the road about five miles.
and mean exactly the same place.
When someone tells you to go "down there for the International Terminal" they don't necessarily mean literally down as in on another vertical level unless the terminal happens to be on another vertical level. They could probably just as easily have said "up there for the International Terminal" — or even "over there for the International Terminal."
Prepositions may also be used as mild intensifiers. Instead of saying "Get out of here," someone might colloquially add emphasis with a few supererogatory prepositions: "Get on up out of here." Paradoxically, those same prepositions could be used to soften the statement as well. Much depends on context and tone.
As any good dictionary will show you, up and down both have many meanings beyond those related to location in a vertical plane. When someone gives a direction such as the one you mention, the words are usually accompanied by a gesture or a movement of the head which should remove any doubt about what is meant.