Sturdy is a gear perk that keeps you on your feet when enemies hit you with melee attacks. Being knocked down leaves you open, so this helps in close fights with brawlers.
Melee hits no longer put you on the ground. You keep shooting or moving instead of losing a few seconds.
Wear one of the listed boots or shoes in the feet slot. Gear perks are fixed to the piece of clothing that carries them, so you get this one by wearing that piece, not by unlocking it in a menu.
Useful in melee-heavy fights and on builds that push into close range. If you play at a distance, another feet perk will do more.