The target for the attack is whichever Pokémon (except for the one using the attack) has the least HP remaining on the in-play zone of both players. Bring Down may target 1 of the player's own Pokémon if the opponent's Pokémon all have more HP remaining than it.[1][2]
If there are multiple Pokémon in play that are tied for having the least HP remaining, the player chooses 1 of them to Knock Out.[1]
If the only valid target for the "Bring Down" attack has an effect on it that prevents any effects of attacks done to it (eg. having Mist Energy or Unown G attached), the target will not be Knocked Out and the "Bring Down" attack does nothing.[1]