White matter is one of the components of the central nervous system. Its main purpose is to connect areas of the brain together, by carrying impulses on neurons. Think of them as cables that link parts of your brain. The reason it is called white matter is because there is a layer of fat that covers the neurons to protect them from harm.
There are several "white matter diseases", including multiple sclerosis, which is the most common in younger adults. In older adults, other neurological diseases, such as Alzheimer's dementia, can also cause changes in the white matter, from the build-up of amyloid plaques in the brain.