宫口 is the obstetrics term for the cervical opening, used routinely in delivery-room language.
宫 here is short for
子宫 (zǐgōng, womb / uterus, literally 'child palace'). Cervical dilation is measured in
指 (zhǐ, fingers) in colloquial speech and centimeters in medical records — full dilation is about 10cm or '
十指 (ten fingers)'.