It means how many times that specific Pokémon has dealt the final killing blow to attacker's last (6th) Pokémon and thus failing his attack.
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I figured this is what it means, but it doesn't seem to make sense. I've cleared out a gym before, and when I placed my own pokemon there, it already says "battles won 1".
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It's over the course of their life and transfers from gym to gym. Wish a pokes battle stats were more in depth.... Would be pretty cool to see their stats as a battler and defender.
Alerts when someone is a attacking one of your pokes would be awesome as welll!