The colour of the nail bed can be useful in assessing the amount of oxygen in the blood and the circulation. There are machines that can measure this but an experienced medical worker can gain much information from looking at and touching someones hands.
I think it's because the colour of the skin under the nail can tell the anaesthetist if there are problems while you are under anaesthetic. But I'm no medic so someone with more expertise than I have should be able to confirm this - or not.
//You'll need to remove all make-up and nail polish before your operation as the doctors will need to see your skin and nails to make sure your blood circulation is healthy.//
I went for an op and had Shellac on my toes which is a nightmare to remove. The Anaesthetist tried to get it off but it wasn't happening. He told me not to worry because there were plenty of other ways to check I was still alive! Then told me count back from 10! :/