Dogs are masters at perceiving their environment through stimuli. Smells, sounds and movements attract their attention and often trigger automated behaviours. For example, when a dog perceives a strong odour or sees a moving object, so-called motivational circuits are activated in its brain that focus it on the object. These circuits are closely linked to the dog's reward system and make it difficult for him to concentrate on anything else.
The "off" signal intervenes in precisely this process: it prompts your dog to take his attention away from the current stimulus and focus on you instead. This is particularly challenging as your dog is following a natural behaviour at this moment - such as exploratory behaviour or the desire to secure a resource.
In cynology, this behaviour is described as stimulus fixation: A dog that is fixated on a particular stimulus needs clear and positive guidance to break away from it. This is where the "off" comes into play. For the signal to work reliably, your dog must learn that cancelling his action always brings him an advantage.
Your dog's brain is designed to process stimuli quickly and efficiently. Particularly exciting or new stimuli activate the limbic system, which is responsible for emotions, motivation and basic behaviour. This system decides whether a stimulus is important enough to pursue - for example, a ball suddenly appearing or the smell of food.
A well-conditioned "off" signal helps your dog to interrupt this natural reaction and consciously choose a new action instead. However, this requires practice, as your dog's brain is initially programmed for the stimulus.
Impulse control also plays an important role: dogs that learn to control their reactions to a stimulus can listen to a signal such as "off" even in difficult situations. Impulse control is not an innate ability, but must be specifically trained - primarily through repetition and positive reinforcement.