That's peer pressure. They don't want to look weak or afraid in front of their friends, so they put on a tough-guy persona. As for how to 'describe' it, I'm not sure describe is the right word. Hopefully you're showing it rather than telling it. And you would do that by showing what the character is like when his tough-guy friends aren't around, and then what he's like when they are. His behavior changes drastically as soon as one of them is in the room, and maybe people say that. They might wait til the friends are gone if they like the character, or if not they might say it while they're still in the room to embarrass him in front of them.
bravado? Depends on the situation, personality and why he feels the need to stand out that way. I knew a short aggressive guy who was always shooting off his mouth. He had been dumped by his parents on his grandparents which always had him on the offensive so that he never had to deal with defending his situation, as nobody dared bring it up.
I think a characters personality is something you want to show rather than something you want to describe. Their personality should come out via the story. Saying they act tough when their friends are around doesn't really say much in terms of their personality. In fact, it's very common for people to act a certain way in certain company, though, not always the example you've given here.
Deadrats, is right. To show what you say you want for the character, I would suggest you position one friend as a confidant. Then you can show the personality contrast in dialogue.
