Emotional stoicism, confidence in oneself and courage.
I would say that those three things, applied broadly, are what people think about when talking about masculinity.
Louis CK did a skit in his show that I found horribly true to life and highlights how absurd the pressures of being masculine are in the modern age.
He's taking a woman out on a date and they have a great time, ending the evening in a cheap pizza place which Louis recommends. After they sit and begin to eat, a group of rowdy kids, near college age, come in and generally disrupt the vibe, are loud and obnoxious, make Louis' date uncomfortable. Noticing this, Louis does what he feels a man in this situation should do, he tells them to be quiet. I don't think he shouts or curses at them, he just asks fairly politely for them to keep it down.
Aftet a pause the alpha of the group suddenly comes over and stands by their table, it's silent now, and he's staring at Louis. He's stood uncomfortably close and waiting for Louis to look at him, his face is impassive, it's a challenge and a threat. Louis talks with him, asks him what the problem in, still being civil and polite, he obviously understands what's going on. The kid clenches his fist and shows Louis the scars and scabs on his knuckles, telling the couple about how much he enjoys beating people up; he affects a mock sympathetic face and tells Louis that he really doesn't want to beat him up in front of his girl but unless he gets an apology he's going to have to. After some back and forth tension, Louis understands that he can't talk his way out of the situation, he's left with two options. He can be brave, macho and rise to this kids challenge, fighting him in front of his friends and his date, no doubt losing physically but also losing dignity, considering the age difference and how foolish he'd look scrabbling around with a group of boys as a balding middle aged man. Or he can apologise, conceding his inferiority to this kid, giving up his ground and accept his place as the beta male. He does, of course, choose the latter and gets laughed at along side a mocking handshake from the kid. The date ends with the woman he's with looking uncomfortable, after some probing from Louis, she admits that she's not sure how she feels about him now. She agrees that he did the right thing and that it would have been stupid for him to fight, but then she scrunches up her face and says "but I don't know..." there's just something illogically irreconcilable about her feelings towards him now; she's witnessed her date show his belly to the aggressor, when everything about our view of masculinity says that he should have been assertive, courageous and steadfast.
I don't find Louis CK that funny, his self deprecating gets old, but I thought that this episode was interesting, really got the absurdity in our choices as men spot on.
Holy shit this post got long, but yeah I recommend you watch that scene user.