When a unit uses the Trog faction ability to go Berserk, the player loses control over the unit's AI, but the unit gets improved attack and initiative. The description says that berserk units never cast spells, and an intuitive expectation would be that a berserk unit should charge and attack with little to no regard for its own safety.
This is not the case in the game right now -- as far as I can tell, Berserk units act like any other AI-controlled unit, complete with spellcasting. Playing as Yithril, I've seen trained units stop short of the enemy to defend (even though they were in range to attack and other units were in imminent danger from the enemy they were ignoring) and retreat from a lone stunned enemy (Bocco nearly one-shot one of my berserk units with bash, and it fled from him on the turn he was stunned only to return after his stun wore off and get killed).
The most striking moment, however, was when I hit berserk on Warlord Verga himself, and he promptly started casting Wither, a spell that takes two turns to cast and applies a minor debuff to the enemy team. While the description on berserk may not specify that units must attack when able (even if that is implied by the concept of the ability), it definitely says they "never cast spells". So this is clearly not working as intended.