The long debated protein dynamical transition was recently found also in nonbiological macromolecules, such as poly- N-isopropylacrylamide (PNIPAM) microgels. Here, by using atomistic molecular dynamics simulations, we report a description of the molecular origin of the dynamical transition in these systems. We show that PNIPAM and water dynamics below the dynamical transition temperature T d are dominated by methyl group rotations and hydrogen bonding, respectively. By comparing with bulk water, we unambiguously identify PNIPAM-water hydrogen bonding as mainly responsible for the occurrence of the transition. The observed phenomenology thus crucially depends on the water-macromolecule coupling, being relevant to a wide class of hydrated systems, independently from the biological function.