The Eagle and Jaguar helmets were given to the military orders of Cuacuahtin and Ocelomeh respectively.
A soldier would be permitted into the eagle and jaguar warrior orders after they had taken at least 4 captives in battle. Even common soldiers could be admitted into these ranks, and they would be granted the honor of becoming a meritocratic noble, as would their lineage. In addition to the standard arms and armor granted to warriors of either rank, the soldier would be given a wooden helmet in the shape of a Jaguar or and Eagle, depending on which order they joined.
Theoretically, there was no difference between the two orders, but based on tributary lists of equipment and general depictions of these ranks, Jaguar knights were probably more common.
The helmet was constructed of hand carved wood and would have been made within Tenochtitlan itself, or delivered as tribute to Tenochtitlan. The jaguar helmet featured a long headdress of feathers fastened to the top of the helmet, while the eagle helmets appeared to have been completely covered in smaller feathers.
The fact that there was a lower “jaw” affixed to the bottom may mean that a chin strap was unnecessary to keep the helmet on the soldier’s head. The helmet wrapped entirely around the head and it could have been padded with a layer of cotton, allowing for a properly fitted helmet to fit snugly without the need for a string or strap. That being said, no depiction or source that I am familiar with mentions whether or not chinstraps were included in the helmets. The helmet likely would have stopped Macuahuitl cuts and light spear jabs completely, and would have helped to protect the user’s head from blunt force trauma.
In addition, the helmets were probably tough enough to stop sling thrown stones and possibly even arrows. The “snout” or “beak” of the helmets would have allowed the user to lower their head and shield their face from melee attacks and incoming projectile fire. The sloping construction of the eagle helmet in particular would have deflected projectiles away from the face.
In addition to the obvious advantages that these helmets gave, they don’t appear to have uncomfortably restricted the wearer’s line of vision, given the wide opening that the user’s face is visible through.