The corpus callosum is the largest white matter structure in the mammalian brain. It consists of mostly of contralateral axon projections. It appears as a wide, flat region just ventral (below) the cortex. It is missing in monotremes.
The corpus callosum connects the left and right cerebral hemispheres. Most (but certainly not all) communication between regions in different halves of the brain are carried over the corpus callosum.
See also alien hand syndrome and split-brain.