The majority of the cells in the brain are *Glial Cells,* not neurons (the cells that actively transmit information.) Glial cells work to nourish and support the neurons themselves, and may help with short range cell signalling.
While it's true that mature neurons as well as mature glial cells do not divide, new cells are constantly being produced by Neural Stem Cells. These cells are constantly dividing to produce new glial cells and in some areas of the brain, new neurons.
So, the majority of brain cancer types involve abnormal glial cells. It also needs to be said that tumors themselves have stem cells. So it is ultimately the neural stem cells that become abnormal, begin dividing out of control, and produce abnormal, malignant glial cells.
The action of neural stem cells is important because glial cells generally have a shorter life span than neurons (but they are still quite long lived compared to other tissues in the body.)
Moreover in some areas of the brain, new neurons are produced by neural stem cells. This is important for such things as long-term memories, spatial navigation, and learning new skills.