Thanks for your fascinating question.
Most cells in the human body duplicate themselves through mitosis and do so many times without issue. Sometimes, however, a mutation occurs in a cell that causes that cell to duplicate itself uncontrollably. These cancerous cells then might then form a tumor that invades and destroys other, normal cells. Neurons are special cells that link together to transmit information and respond to the world around us. Also, neurons do not undergo mitosis and so rarely become cancerous as they do not duplicate themselves.
So what cells are responsible for brain tumors? Turns out the brain contains another type of cell called glial cellsthat give the brain its structure and supply neurons with oxygen and nutrients. In fact, there are by some counts just as many glial cells as neurons in the brain. It is these glial cells that are responsible for the majority of brain cancers, especially given genetic or environmental risk factors like smoking. Brain cancer can also occur when cancer cells in another part of the body metastasize, or spread, to the brain.
On a final note, it’s often stated that new neurons are never produced by the brain. However, recent evidence actually suggests that certain brain areas in fact do produce new neurons from stem cells well after birth. These brain regions are the hippocampus (which is responsible for long term memories) and the olfactory bulb (which is responsible for the sense of smell).