Arbitrary danger is danger that is essentially meaningless. For instance, if a comet is about to strike a planet, that is very dangerous, but it is arbitrary and pointless in an RPG in which no one can detect or do anything about it, such as most settings that do not feature superheroes, superscience, or world-shattering sorcery. Similarly, if there is a forked hallway, and one hallway leads to wealth and the other to almost certain death, that is the very definition of arbitrary. Why is one course better than the other? Arbitrary danger is a problem in RPGs because it detracts from meaningful choices.
Compare to the concept of Nintendo Hard.