The Boots of Hermes were depicted as greaves with burning red wings on them. Kratos mercilessly amputated them out of the legs of their owner; the Messenger God, Hermes. Those greaves allowed Kratos to move at great speed, ramming through enemies and throwing them aside, and the ability to run along the sides of walls. Those walls were always marked with shining and golden bootprints. When not in use, the wings on the side coiled themselves around the Boots. They weren't among the scattered items at the end of God of War III, and could still be seen on Kratos's legs.
In the Fear Nothing Trailer, Kratos used the Boots of Hermes to run alongside a rocky wall and attacked a Centaur General, by jumping off the wall and hooking onto the Centaur General with the Blades of Athena. That way of attacking Kratos' enemies wasn't present in the final game.
The Boots could be seen in the trailer for God of War on PS4. At the beginning of the trailer, they were on the chair to the left just inside the door when Atreus entered the house.  However, in God of War (2018) in-game version, the Boots of Hermes are nowhere to be found.