A turn is everytime that you get the option to do an action, whether it be, using a move, an item, or switching your Pokemon. Sometimes, turns go by without you using an action, usually if you are under the effects of moves like Outrage, Petal Dance, or have to recharge after using a move like Hyper Beam, Giga Impact, Blast Burn, Frenzy Plant, Hydro Cannon, or Roar of Time.
So in a horde battle, unless you use a move like Outrage or Hyper Beam, every time that you get the option to use a move, 1 turn has gone by.