The standard height to install a towel rack in a bathroom for adults is about 48 inches from the floor. For a child's bathroom, about 36 inches from the floor is appropriate.
Installing the rack at a different height might make sense for decorative reasons. For instance, a homeowner may feel the look of the bathroom flows better if a towel rack is installed at around the same height as other features in the room, such as the top of a vanity table surface. Installing a rack higher than 48 inches off the floor creates an uncomfortable reach for most adults.