Can someone explain how gender pronouns work

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What does it mean when someone's pronouns are "she/they" or "he/they"?

I don’t want to make this topic about a specific individual, so I won’t name names unless it becomes important to refer to a specific statement. In general, when one describes one’s pronouns, it seems the standard to list both an object and a subject pronoun: “he/him”, “she/her”, or “they/them”. That’s a bit of a curiosity in itself – why list both? – but not the main thrust of my question. Lately, some people have announced new pronouns and have listed two subject pronouns, a gendered one and…