The creature is activated multiple times.
When a creature is activated, it attacks if it can attack, it uses it's passive abilities if it can and it's frozen/delayed counters are decreased by one. And it takes poison damage if any.
Just keep in mind that activating a creature and activating it's active ability are two different things.
I just don't like calling adrenaline's effect 'multiple turns' since:
- It can only use it's active ability once even if adrenalined (but freeze and delay prevent that!)
- A turn is something the player has, not something the creatures have.
For example, using M:tG terms, we would say that the creature has multiple 'attack phases', as well as multiple 'passive ability phases' and 'decrease counter phases' and 'receive poison damage phases'. But a turn consists of a number of other phases too, eg. the phases when player can activate the active abilities, the phases when a player can buff the creature or use other abilities/spells on it, etc. For example, even if you adrenaline a creature the same turn you play it, it still has summoning sickness (you can't use the active ability). So, the 'enable active ability' phase, which usually takes place once at the beginning of each turn, is not repeated by adrenaline. Generally any phases with player input are also not repeated. Thus the effect of adrenaline is entirely different from what multiple turns would be.