It depends on your state, and whether your unpaid tickets rise to the level of a misdemeanor. Years ago in California, I had two unpaid tickets that resulted in warrants being issued for my arrest, charging me with misdemeanors rather than infractions (which is what most traffic citations are considered). They didn't make a huge effort to find me, but when I finally turned myself in I had to pay a huge fine (I borrowed the money from my mother, which was like pulling teeth) and was told that I'd go to jail the next time I didn't pay a ticket. So, this can be serious stuff.
If you have unpaid tickets, chances are your driver's license has been suspended and/or there is a warrant out for you. These have to be reported to the BON. As 'crimes' go, this isn't a bad one and you probably won't be denied a nursing license on the basis of it alone, but you should make every effort to clear it up before you apply. Take a temp job at night if need be, or borrow the money, even if you have to resort to begging from a friend or saving up pop bottles and cans. You can also contact the court to see if they'll let you do a payment plan.
Good luck to you. I've been in your shoes and it's not fun.