The long band of nerve fibers that connects the brain's hemispheres is:

 The answer is Corpus callosum. The largest structure of the human brain, consisting of the two cerebral hemispheres connected by the corpus callosum and covered by the cerebral cortex. Corpus callosum is a long, thick band of nerve fibers that connects the left and right hemispheres of the brain and allows communication between them. Development of the CC makes communication between the hemispheres more efficient.