The corpus callosum is a large white matter tract that connects the two hemispheres of the brain. The only way the two cortices can communicate with each other is through the corpus callosum- above the corpus callosum is not connected, so you can actually separate the two hemispheres down to the corpus callosum with your hands (once the meninges have been removed). Here, part of the cortex has also been removed so that there is better visibility for the corpus callosum- it’s the part in the middle of there brain there that looks like a band. When it is severed, the brain can compensate fairly well and the individual will appear completely normal and functional, until they are doing certain tasks with one side that does not have that capability (for instance verbalizing something that they see only with their left visual field, which is processed on the right side of the brain, when language is contained on the left side of the brain- a task that would require the two sides to communicate).
[Image found here]