Sexism doesn't necessarily mean that you hate someone simply because of someone's sex or gender. It is any view or action that comes against the equality of all gender identities and sexual orientations.
The most famous example would be women in workplace earning less than their male counterparts. However, cases such as rape can be results of sexism, as well. The idea behind is that if a man rapes a woman, his motive can be his so called superiority.
When you think about it, phrases such as "to man up" or "being a sissy" are examples of everyday sexism that we are mostly unaware of. The roots of this problem are so deep that a lot of things need to be written down anew to deal with sexism.
Someone's gender identity never makes that person superior to others. Everyone's equal, and we should remember it that way.
By the way, sexism can be against all gender identities. The form of sexism we see mostly is targeted against women and queer people; however, there is also a type of sexism which is targeted at men; it is called misandry.
Commonly it's referred to Discrimination of a person based on persons sex.
Sexism is a pretty widely used term right now. Sexism means to hate a person based on their sex. Let me give you an example, so you can understand it better.
For example, a person likes male singers even though their voice is bad and they hate female singers even though they have good voice. I know it's kinda awkward way to explain it but that above situation means that the person is sexist towards womans.
This word is mostly used for man who think women can do much because they are "women". They don't believe in gender equality.