This is the best explanation I've seen on the meanings of cisgender vs transgender and why we use these words to describe someone's gender.
... Cisgender refers to people who experience and present their gender in a way that’s aligned with the gender of their body. It contrasts with transgender, which refers to people who experience their gender as different from the physical gender they were born to.
... The prefix cis means “on the same side” while trans means “on the other side”.
... The reason that the word cisgender is important to use is that it takes away the idea that being cisgender is “normal.” When we assume that man = cisgender man unless we use the term transgender, we reinforce the idea that cisgender people are normal and transgender people aren’t. Of course, being cisgender is more common but when we use language that reinforces the idea that more common equals normal, we marginalize people who are well within the range of diversity that exists in the world. (Read more)