The Nurse Hat, as the name implies, is a typical white nurse hat with a red cross. There is a thin red line around the brim of the hat. In EBF5, both the cross and the line got changed to pink instead.
It gives an average amount of Defence and Magic Defence to the wearer (and in EBF5 also a very slight boost to HP and Magic Attack at max level), boosts their healing spells, and gives them Syphon resistance, as well as Death resistance in EBF4 and EBF5 (EBF5 also gave it Holy resistance).
While the hat originally depicted a red cross in EBF3 and EBF4, Matt eventually found out that utilizing red crosses in videogames violates the Geneva Convention, which is why the cross got changed to pink instead in EBF5.