Nothing. It just means there is nobody for them to discuss your treatment/situation with and if you are not in a position to discuss your treatment with the staff they will proceed in the way they believe is in your best interests
I think one of the reasons they ask for next of kin is if you were perhaps taken into hospital and unable to tell them they could look in your notes and phone that person who is listed as next of kin.
If there is no next of kin, then I expect you would ask a close friend if you could give their details in case the hospital needs to let someone know where you are.
Barry is correct. Just ask the person you feel is right and ask them if they are prepared to act as next of kin. You can change your next of kin any time you like. There is no legal standing. But do ask if they are prepared to do it.