Polarized hull plating was a defensive armored hull technology used on shuttles and starships. Before the development of deflector shielding, hull polarization was the primary defensive measure for starships against enemy weaponry.
In the 22nd century, this technology was used by Earth starships such as the J-class, NX-class, Freedom-class and on smaller auxiliary vessels such as the shuttlepod. During the months Enterprise was in the Delphic Expanse, polarization technology on Earth had been improved by 12%. (Star Trek: Enterprise; ENT: "Horizon", "Vanishing Point", "Home", Star Trek Beyond)
In the 24th century, starships still occasionally polarized their hull plating, though not typically as a defensive countermeasure. One example was disrupting a tractor beam lock by rotating the frequency of the hull plating's electromagnetic field. Ships also sometimes polarized their hull plating to help mask their sensory signature, which worked by interfering with enemy sensor scans. Polarizing the hull was also done by downed vessels to help their mothership locate them. (DS9: "In Purgatory's Shadow"; VOY: "Once Upon a Time", "Equinox, Part II")