Talk about how dedicated you are to nursing, how much you regret failing and how you will try harder (give examples). State that you very much want to learn and how you have always wanted to be a nurse. If you failed because of some crisis during that part of your life, perhaps you could mention what it was, and how it affected you back then. Then state how it is not a problem now and what your solutions were, etc.
Take full credit for your failure...never make it sound like it was someone else's fault that you failed (even if you think it was), that will turn them off to you. If you have since studied up on the material from the class you failed, tell them that. If you haven't studied it, you should. Basically, admit your mistakes, then tell them how you've solved them (and learned from them).
You can, of course, lie. I'm not saying you should lie through your teeth and make it over the top, but even if you hadn't wanted to be a nurse for as long as you can remember, it wouldn't hurt them to think you have. :-)
And DEFINITELY make sure you proofread
it. Many people are negatively swayed by spelling
and/or grammatical errors.