Hi, usually babies have 3 vessels in their unbilical cord- 2 arteries and one vein- usually there is no significant threat to baby's health and they are born fine- but what the major risk is during delivery. Dr's are worried that the cord wont be able to withstand the pressure during contractions or when baby passes through the birth canal. Most babies are usually fine; the dr's just take extra care when monitoring the baby to make sure baby's heart rate doesn't drop.
So how does all this apply to you and your triplets?
Well, since you are having triplets you are most likely going to have a scheduled c-section to deliver all the babies- I would say 99.9% of hospitals do c-section for triplets- and in that case there is less likelyhood for any kind of compromises on the cord because the c-section usually occurs before contractions have started and the babies wont be delivered vaginally, so there's no worrry there.
I hope this answered your question- and I would suggest that if you have any more concers to talk with your dr about it.
And good luck with your growing family.