Once you have a Neuralink set up like this, the idea is that the brain could be connected with an external computer, and information could flow back and forth between the brain and this external computer. Musk talks about this external computer as the ‘third brain’. The “third brain” language is coming from his perspective that we already have two brains: our limbic system which deals with our emotions, and our cortex, which developed later, and which is where thinking and planning happens. Your third brain would be an external computer, perhaps housed in a data center somewhere, with which you would communicate wirelessly.