Toxic masculinity is a psychological concept where long-established social norms from generations of use are causing harm to others in society and to the men themselves. Some of these harmful ideas include things associated with being an "alpha male", who dominates others around them, denigrates and demeans women, acts homo- and transphobic, and hiding emotions.
These ideas have been around for ages. I was reading a lot of short horror fiction written by women for an MFA class. Back in the 1800's, even the women were writing patriarchical stories where the men were the strong, silent types who took care of things whilst the womenfolk swooned on the settee. Men didn't cry unless they were effeminate, and some outright equated emotional men to women -- and it was meant as an insult to the men.
Look at all the tough "male role model" movies. John Wayne. Humphrey Bogart. Clint Eastwood. All grizzled, tough gents you wouldn't want to get into a fight with, who were completely self-sufficient and relied on themselves to get through every disaster. People crossed them and the guns came out blazing. Even songs like Jim Croce's "You Don't Mess Around with Jim" or even "Bad, Bad, Leroy Brown" filled the airwaves with a message that men were only men if they followed the path of the obnoxious.
The homophobic and transphobic mentalities have deep roots in toxic masculinity in that it is the antithesis of what it means to be an alpha male. Some fear that even being friends with "one of those people" will make their shiny male armor crack. The concept of liking someone because of who they are as a person gets lost in the fear of getting associated with the wrong crowd. It's a social problem that prevents a lot of individuals from being understanding and allowing for differences.
Then there is the issue with treating women horribly, as shown recently with the #MeToo movement. Harvey Weinstein wasn't the first to treat women like playthings for sex. Heck, just look in gaming channels where kids -- young kids -- threaten others with things like rape and murder. If their mothers heard them saying such mind-boggling stuff they'd take away their PlayStations and sell them on eBay. The PlayStations, not the kids, although I'm sure they'd be tempted...
Toxic masculinity issues can only be addressed in the smallest unit, the family, to really change the culture. It's going to be a long while until it starts to fade out. In the meantime, it's up to us to point it out when we see bad behavior, especially with our own spheres of influence.