A prolapsed cord is when the umbilical cord manages to get in the way of baby’s exit and slips into the birth canal first — usually when the water breaks. Baby can push against the cord during labor, compressing it so that less oxygen is making its way to your little one. This is very dangerous for baby, and might require an emergency c-section. If you think you can feel the cord in your vagina after your water breaks, get on your hands and knees (to reduce as much pressure on the cord as possible) in the back seat of the car while someone rushes you to the hospital, or call 911. Your doctor will most definitely want to get baby out right away.
Prolapsed cords are more likely to occur with premature labors or with breech vaginal deliveries, but they are very rare (about 1 in 1,000 deliveries), so your chances of having to deal with this are slim.