I think it has its uses but it doesn't make sense to a lot of cisgendered people because they just can't visualise what it means. So I use a slightly different analogy that is a bit easier for them to understand: weight. Because it's easier for a cisgendered person to understand feeling like a 'thin person trapped in a fat person's body'.
This is what I tell them: imagine you've been naturally thin all your life. You're a thin person, everybody sees you as a thin person, you wear thin people's clothing, and nobody thinks any less of your lifestyle choices or presumes them to be unhealthy. Society reinforces your perception of yourself as a thin person and because society prefers thin people, it sees you as being normal. So in your mind, as well as your body, you see yourself as being a normal, thin person.
But imagine you then fall ill or are prescribed medication that makes you unexpectedly balloon in weight. You still feel like a thin person inside because your mind still sees you that way; that's your identity and it always has been. But when you look in the mirror, you're shocked by what you see - all of a sudden your body doesn't match the thin person you know yourself to be. Suddenly, everyone else sees you as being a fat person. They presume you're lazy, they judge the food you purchase, they question your lifestyle choices.
But that's just not you, and you hate looking and being treated like something you're not. It makes you feel very uncomfortable. You can't change your mind to be happy with being an overweight person (because that's not who you are and you dislike being overweight) so your only choice is to fix what's gone wrong with your body. So you change your meds, you go on a diet, you join a gym, maybe you have some liposuction... and slowly but surely you bring your body back into line with how you see yourself so that you can be at peace living in a body and mind that match.
Can you picture that feeling? Of feeling like you're one thing, but having society treating you like something else because your body gives them an inaccurate picture?
Well, that's how I feel. Only I've always known I'm male, but the mirror and society sees something else; something that I've never felt inside. The only way of fixing that is to correct my body, because I can't change my mind. I'm working on fixing this, any way I can, so that I can be at peace living in a body and mind that match.