Informally, we define a projective DAG to be a DAG where all arcs can be drawn above the sentence (written sequentially in its original order) in a way such that no arcs cross and there are no covered roots (although a root is not a concept associated with DAGs, we borrow the term from trees to denote words with no heads in the sentence).
nonprojectivity is predictably more wide-spread in DAG representations, since there are at least as many arcs as in a tree representation, and often more, including arcs that represent non-local relationships.