When turned on, the dome of the Van de Graaff generator becomes charged (either positive or negative depending on its design). Anything in contact with the dome also gains the same charge. If a person holds the dome, they will become charged and their hair might stand on end if it is long and dry enough. If a bit of fur or similar material is set on the dome, the hairs will stand on end. Each individual hair has the same net charge as the rest of the fur and the dome. Since like charges repel, the hairs are pushed away from each other and the similarly-charged dome, causing them to stand up.
Under the right conditions, the fur may even fly off the dome if the electric force exceeds gravity.