This is a problem primarily experienced by women as the female tailbone is more flexible and commonly also more sensitive than the male tailbone.
When in a very upright position, the tailbone can be very close to the saddle. In combination with a too soft or too narrow saddle this can lead to discomfort and pain.
The pelvis is held together by ligaments. When there is tension in the pelvis, these ligaments can excert a high strain to the tailbone.