Generally, if 'hier', 'da' and 'dort' are used to designate
place of varying distance, then - 'hier' refers to closest
proximity - 'da' refers to a larger distance from the speaker -
'dort' indicates largest distance. Imagine you talk to someone
within an interesting park full of interesting features. 'Hier
stand die alte Mauer der Stadt, da war der Wachturm, und dort
(drüben) war das alte Rathaus' However, nobody takes it as
strict. In particular, 'da' and 'dort' are often used
interchangably. These rules do not cover idiomatic usage (e.g.
phrases like 'hier und da'), or you may completely dismiss the
distance rules if you refer to a couple of locations and don't
want to repeat the same word over and over again. (When revering
to a map:) 'Hier ist die Autobahn A3, dort sind wir, und da war
ist die Raststätte wo wir gestern gegessen haben'. For more
information about the (lack of) difference between 'da' and
'dort' see this article published from the Philologisch-
Historische Fakultät Universität Augsburg.