Here's how I've explained it to a small child. It's a lot of information to cover, even being oversimplified, so it was broken up into smaller conversations over time. Not being familiar with your younger relatives I can't advise on how many parts to break this up into, but here's the gist.
Most people think they can always tell by looking at someone, whether they're a boy or a girl. But it's not always that simple. If someone says they are a boy, or a girl, it's important to listen to them, no matter what they look like.
Sometimes people are born with a body and brain that don't match. They might have a boy brain, but the kind of body a girl usually has, or a girl brain, but the kind of body a boy usually has. This makes their body not feel right for them, and means people might look at them and think they're a girl but they're really a boy (or vice versa here, you get the idea). They might get help from doctors to change their body so it will feel right to them. They might take certain medicines. They will start to look and maybe sound different (give some child-friendly examples like growing a beard), but they are the same person.
You might need to specifically spell out for them stuff like, "For boys/men we use the words he, him, his, and sir, and for girls/women we say she/her/hers and ma'am" or "Sometimes people don't like their name. When they are an adult they can get it changed. I'm changing my name to ____"
