Bravery
The Bravery stat is a measure of how brave a unit is in the face of danger. A higher bravery score reduces the amount of Morale lost due to morale-decreasing events, so a brave unit (alien or X-COM) has less likelihood of panicking or going berserk during combat.
Stat Range
New X-COM recruits will always begin with a value between 10 and 60. Due to the way the Bravery stat is stored in the data files, it will always be a factor of exactly 10. X-COM soldiers' Bravery is capped at 100, although tanks and certain alien races can have a Bravery of 110. Unlike other stats, Bravery cannot overflow its cap because it can only increase by one unit at most per combat mission.
Improvement
When a unit's Morale drops below 50, it has a chance of panicking or going berserk (see Morale#Panicking_and_Berserking for full details). If a unit successfully resists panicking, it will gain a "bravery experience" point. For each bravery experience point gained during a combat, a unit will have an additional 10% chance of gaining a point of Bravery at the end of the mission, up to a possible 100% chance with 10 (possibly 11) bravery experience points.
Bravery and Psi Attacks
Psionic panicking attacks will reduce a target's morale by an amount dependent on the unit's Bravery. Although Bravery will not make a unit more psi-resistant, particularly to mind control, high Bravery can greatly reduce the impact of panicking attacks performed on that unit. See Morale#Psionic Panicking Attacks for full details.