Zen Mode triggers when Darmanitan (any form) reaches below 50%, in which case Darmanitan transforms into its Zen Mode Form. Zen Mode Darmanitans has different stats from the base forms: Unovan Zen Mode Darmanitan is a slow Special attacker, while Galarian Zen Mode Darmanitan is a blazing fast glass cannon. Zen Mode Darmanitan also has different typing than normal Darmanitan.
Additionally, if Darmanitan is above or equal to 50% health, it will revert to its base form. This means that if you have an item like Leftovers or a teammate with Heal Pulse, you can revert a Zen Mode Darmanitan back into base form Darmanitan.
Zen Mode cannot be suppressed or copied inside battle. This means that, among other moves, Worry Seed, Entrainment, Gastro Acid, and abilities like Trace will fail on a Zen Mode Darmanitan. Note that prior to Gen 7, Zen Mode CAN be suppressed by Gastro Acid; if that happens, the Darmanitan reverts back to base form regardless of which form it was in and is unable to change forms.
Sources:
https://pokemondb.net/pokedex/darmanitan
https://bulbapedia.bulbagarden.net/wiki/Zen_Mode_(Ability)