A Turn is a sequence of Activations made by the side whose Turn it is, either the Hero Players (collectively), or the Overmind Player. During a Turn, special abilities may trigger or be used which may allow the other side to make an out-of-turn Action or Activation of a Model/Unit, but that doesn't change whose Turn it is.
In particular, the Overmind Player has an ability that once during the Hero Players's Turn allows the Overmind Player to discard two Mutation Cards immediately before a Hero's Activation, and Activate one Alien Unit first.
Note: the rulebook and some card texts sometimes uses the word "Turn" a bit loosely to also refer to the Activation of a a single Hero or Alien Unit.
During the Hero Players's Turn, all the Hero Players activate their Heroes on at a time, in any order they choose.
Activation
An Activation normally consists of selecting a Hero or Alien Unit and taking up to two Actions with it. Each Hero and each Alien Unit can only be activated once during a Round, unless some special ability says otherwise.
When a Hero, Alien Unit or Blip Token is Activated, discard any unused Overwatch token it may have, then take two Actions. The actions available are Move, Sprint, Melee Attack, Shoot Attack, Interact, Overwatch, and for Blip Tokens: Flip Blip Token.
Note: an out-of-turn Activation still counts towards the once-per-turn limit, but a triggered Action that happens without an Activation does not. Consequently, for example, the Overmind Player's Interruption ability, which lets it activate one Alien Unit during the Hero Players's Turn, means the Alien Unit Activated by that ability can't be Activated next time it becomes the Overmind Player's Turn; but Overwatch attacks and Alien Behaviour Actions don't count as Activations.