Your partner's other partner — someone you're connected to through a shared partner but aren't dating yourself.
The math is simple. If you date someone who also dates someone else, that someone else is your metamour. You're not lovers; you're linked by a person you have in common. Kids raised in blended families already know this shape without a word for it — polyamory just named it.
The common misconception is that a metamour is a rival, a threat, or someone you have to "manage." Sometimes the vibe is exactly that thin. But the term exists precisely because the relationship isn't nothing. How much you and your metamour actually interact is its own spectrum: at one end, "kitchen table" polyamory, where metamours hang out like extended family; at the other, "parallel" polyamory, where you know the other person exists and otherwise never cross paths. Neither is more evolved — they're preferences, not report cards.
What makes the word useful is that it's neutral. It doesn't say friend, doesn't say enemy, doesn't rank anyone as primary or secondary. It just marks the position on the map, and lets the humans decide what to do with it. That restraint is the whole point.