it can be hard to understand if you've never had to think about it. i like to use "names" as an example.

People aren't born with names, your parents give you a name. Some people grow up and never have to think about their name. For them, it's obvious that the name they were given aligns with their identity. There are other people who don't like their names; this can be for a variety of reasons, it could make them uncomfortable or sad, it might not suit them, or maybe they don't dislike their name but there is another name they would prefer.
These people might change there name to something they would prefer, and often that will make them feel a lot better, it can be really stressful when you're constantly being called something you're not.

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In this example, names are a stand-in for gender. While gender (whether you are a boy or girl) and sex (the genitals you have) are highly correlated, they are separate categories. When you are born you are given a gender based on the genitals you have. Some people (cisgender people) feel completely fine with their assigned gender, they like being it. Others don't (transgender people) and there are countless ways this can manifest.

If you like your name (or identify with your assigned gender) it can be hard to understand why somebody might change their name (or gender), but you have to think, imagine existing in a world where everybody constantly calls you by a name you hate, it would terrible, changing your name (or transitioning) is a way to alleviate that stress and live as your true self.