There's some backlash against this term because some (willfully mis-?) understand it to mean men are toxic or that masculinity is toxic. I think it's helpful, particularly for men, to understand what the term means.

To start, we live in a patriarchal society. "The patriarchy" is not all men or even a few concrete men at the top but rather a system of power structures and values that A) divides the genders into men and women and B) empowers men and weakens women to assign them positions as in a traditional patriarchy, whence the name "patriarchy".

To achieve A we're taught to focus on our differences rather than our commonalities. Men are from Mars, women are from Venus. We highlight these (perceived) differences with different dress codes for men and women, different standards for make up, hairstyles, etc. and encourage different behavior down to our speech patterns with gender roles. This is getting into how the patriarchy plays into B:

The inventories of traits and acceptable behaviors associated with masculinity and femininity are set up to make men rise to the top and women sink to the bottom.

Nurturing, soft, beautiful, sexy, friendly, submissive, passive, receptive... these are the traits we assign to "femininity". They're designed to objectify and subjugate women and to make women fit themselves into that system.

Ambition, aggression, strength, intelligence, leadership, dominance... all traits that are coded "masculine" in a patriarchal value system. All meant to empower men.

The pressure from gender roles is therefore such that women are constantly told to be pretty and docile, to keep them in their place at the bottom (in older generations girls were even taught to let boys win in games because they'd be girlier that way and boys liked that..), while men are constantly told to be strong to keep them in their place at the top.

Unfortunately, we can get too much of this sociological doping. "Grin and bear it" strength, taken to the extreme, can lead to bottled up feelings festering and becoming harmful. "Don't take shit" aggression, taken too far, can lead to violence over minor slights. That's when the "masculinity" that's meant to keep men in positions of strength ends up hurting them. It turns "toxic". Hence: Toxic masculinity.

When people bring up this term, it may be wise not to get defensive as if they are issuing an attack on us or even our masculinity. They're primarily pointing out symptoms that show we may be overdosing on "masculinity" and it's hurting us, or making us hurt others!

Aside: It is sometimes brought up that if there is toxic masculinity, there must also be toxic femininity. Feminists already had a term for this before "toxic masculinity" was coined so they still use the older term for toxic femininity: "internalized misogyny". Just as toxic masculinity doesn't describe "bad things men do" but instances where our masculinity is hurting us, toxic femininity is when the pressure to be feminine is causing harm. It makes sense to keep a different term for this, as due to the direction of oppression in the patriarchy, as described above, pressure to be more feminine is always also oppressive, so it doesn't have to especially "turn" toxic to cause harm. It's just misogyny. Or in women's case, internalized misogyny.

The patriarchy isn't just upheld by a cabal of old patriarchs but by everyone in society who perpetuates gender myths and encourages or enforces gender roles, this also includes women. Women also help police other women. In part because we're all caught in a mire of tradition which restricts our thinking, and in part because compliance with the oppressive system yields certain benefits. If you invest a lot of effort into being very pretty, you may not get taken as seriously and you're wasting time and money on appearances, but at least you will reap the benefits of being very pretty. Examples of internalized misogyny include a grandma who calls a younger woman a slut for the way she dresses or a woman telling her friends they're gross and manly looking if they don't shave, etc.