Bravery
The Bravery stat is a measure how brave the soldier is in the face of danger. A higher bravery level results in higher morale on a mission, and therefore, less likelihood of panicking or going berserk during combat.
Starting Values
New recruits will always begin with a value between 10 and 60.
Improvement
You have a chance of +10 Bravery being awarded if your soldier loses control due to heavy morale loss. If your Bravery is improving, it can be due to several reasons. On the one hand, it could mean you're not doing very well and you're losing so many soldiers that the others are panicking. Getting hurt also drops morale. Or it could mean that the soldier isn't good at resisting psi attacks.
Specifically: each time your soldier is panicked or mind controlled, his or her chance of a +10 Bravery award at the end of the mission increases by about 10%. At 10 panics and/or MCs, you have approx. a 90% chance, and at 11 mental breakdowns, the +10 Bravery award is guaranteed.
You can not get more than the lone +10 award in any one mission, even if you panic a hundred times.
Due to the way Bravery is stored in the data files, it can only have/increase in increments of 10.
Maximum Caps
An X-COM soldier's bravery is capped at 100 (but aliens can have a Bravery of 110). Unlike other stats, Bravery will not overflow its cap because it can only increase by one increment at most per combat mission.
See Also
Thanks, User! I put it under "Improvement", above. If we get one or two others confirming, we'll take out my note. Hope you don't mind... I'm just really interested in a confirmation that the game can work some other way that I didn't realize!
By the way... thanks for all your many contributions all around the wiki! Why not consider Logging In (upper right of wiki page) with a user name, so we see what all you've done? Otherwise the wiki gives you a different i.p. address whenever you edit, so we neither know who you are, nor are we able to see all the stuff you (as one person) have done across sessions.
And thanks again for all your stuff! You can delete all my notes here after reading them - MikeTheRed