Berserk State refers to a type of transformation that Demons undergo that sends them into a destructive state of anger and fury.
Every Demon, from the moment they are born, has the capability to trigger this form. It causes them to undergo a transformation that can increase their body size, grow or create new appendages that may further give the user a more intimidating or frightening appearance. Their anger drives them to the point that they are destructive and unpredictable.
Besides the change in body structure, all users receive an ample boost in their natural combat capabilities. Their strength, magic potency and the like become far greater than they were initially, allowing them to easily overpower Demons who would otherwise be physically stronger than them, survive damage far more, and be able to perform more powerful magic spells with ease.
The downside though is that the user is in no control over their actions. Once transformed, they are at the mercy of their own being as they will continue to attack anyone that they happen to be near until they are dead. While their actions can be unpredictable to where it's hard to defend against them, nevertheless as soon as there is nothing left to kill they will often begin self-mutilation, which usually leads to death.
The transformation can only be done if the user's mind is calm or soothed, though in Sakido's case it might just be a matter of rendering the user unconscious in some way so that it can be undone even before the exact moment of death. With Buwaro, he not only had to be put to sleep through magic, but as he got older he more or less needed to have the Star Emblem on him to revert him to normal.
It seems to be possible for the user to maintain control of their sanity by coming into contact with a Star Emblem, either by wearing it or touching it. With Buwaro, even after being forced into transforming by drinking a Red Potion, he still maintained some of his sanity just because he had his pendent still. While it doesn't completely restrain his wild tendencies, he could still act on his own and have simple speech. Sakido displayed a similar action after touching his pendent, and realizing what it could do she kept hold of it while trying to escape in that form.
Tsavo theorizes a possibility that the Red Potion holds the key to unlocking the secret to controlling this form, since it is what can trigger a Demon to go berserk; and being an alchemist he could alter its properties so any user can remain in control.