I believe that this sentence has no satisfactory scientific background.
In fact, it has been said 10% instead of 12%.
This sentence may be based on the fact that our brain is organized in layers, from superficial to more profound. And, from neuroscience discoveries, you can train your brain to use it more in a more superficial manner or more profound. Such as, several oriental cultures teach you to use your brain in a profound manner.
So, if this sentence is correct, it means that you can use your brain more, more efficiently, however, from studies in neuroscience, not from the fact that we have extra compartments in the brain unused. In the image below, adapted from a book in neuroscience, you can see how the brain is heavily used even in simple tasks.
Another possibility is the fact that we can recover from strokes, than we can claim that it is because we have not used our brain in its fullness, but it is due to neural network connectivity.
Therefore this sentence should be seen with caution, not as we have a reservoir of neurons waiting to be used. Initially, it was thought that our brain was divided into specialized compartments, nowadays we know that the brain is "homogeneous", the skills locations is merely a organization, someone that loses their ability to sing can in some cases recover, it is possible not because you have extra brain power, but because the component for the job, neurons, is the same for every section, and the brain works in networks, which is resilient and adaptive.