DAGs are “acyclic” in that they contain no directed cycles: one cannot trace a sequence of arcs in the direction of the arrows and arrive whence one started.
“The future cannot directly or indirectly cause the past.”
Apparent counterexamples (‘schooling and wages cause each other’) are usually resolved by redrawing the DAG with a finer temporal articulation. No “simultaneity.” (There’s theory for cyclical graphs, too, see Pearl 2009.)