This definition really shouldn't be hard to understand if you've got a vague grasp of what the word transgender means, but despite this, some cisgender people are under the impression that it's a slur; explaining to these people that it's about as much of a slur as the word heterosexual doesn't do anything to change their mind on this subject, so you can just safely dismiss these people as not very bright.
Sarah is a transgender woman; she was assigned male at birth, but identifies as female.
Bob is a cisgender man; he was assigned male at birth, and identifies as male. He objects to being called cisgender, stating: "I don't like that some tumblr tranny made up a term to describe me, it's insulting! I'm just normal!" He does not see the irony in objecting to cisgender but being perfectly a-ok with tranny, an actual slur.