The corpus callosum is the most important orbital system for connecting the two brains. The approximately 200 million Comisuren fibres enable the exchange of information. As the example of split brain patients shows, this communication is very important because the two cerebrum halves not only have partly different tasks, they also process information from the other side of the body.
An example: In the visual cerebral cortex, information from the left visual field is processed from the right side. However, we do not see any difference, although we are dealing here with an overlapping of slightly different visual fields in perspective. This shows how important communication between the two halves of the brain is.
https://de.wikipedia.org/wiki/Corpus_callosum (Wikipedia CC-by-sa-3.0)