It's a type of headgear that covers the forehead, the back of the head and sides of the face, but does not cover the top of the head or the face. Having said that, it comes with a few variations.
A. Gambit. A character created by Chris Claremont and Jim Lee. Appeared in “The Uncanny X-Men” in 1990. His headgear not only covers his chin and neck, but also seems to extend to the rest of the costume.
B. Matrix. A character that appeared in the video game “Time Killers”, which was released in November 1992. Her headgear does not cover her chin or neck.
C. Miss Haliday. A character created by Max Autohead and Matthew Hatton. Appeared in “Cyberswine” in January 1995. Her headgear covers her chin and neck, but does not extend to the rest of her outfit.
D. Meanstreak. A character created by Ron Lim and John Francis Moore. Appeared in “X-Men 2099” in 1993. His headgear does not cover his chin, but it seems to extend to the rest of the costume.
What these examples have in common is that they all appeared in the 1990s. I have heard it said that fans generally consider this headgear dated at best and laughable at best. After all, why would you wear headgear if it doesn’t even protect your face or the top of your head?
I just wish I knew what this type of headgear is called.