To add on to manna's explanation:
As stated in manna's quick and rather thorough explanation, many schools require prereq's before officially starting a nursing program. Often times they include anatomy, physiology, microbiology, and some chemistry, as well as other courses required for graduation, such as English, humanities, etc..
Licensing as a nurse varies from state to state. (I live in CA) However, after graduating from a accredited nursing school (either through a hospital, a community college, or a 4-yr university), you are qualified to sit in for the NCLEX-RN. When you pass that, you become a certified RN. (I'm assuming you are interest in being an RN -- LPN/LVN require less time spent in schools than a RN, but they also have to take the boards to get certified.) If you are a graduate of a community college and pass the boards, you are an ADN, and if you graduated with a bachelors, you are a BSN. Usually, most people say that since both RN have passed the same boards and carry the same title, RN, they are paid the same, and treated in same manner. However, these days, more and more employers favor the BSN, and BSN's tend to make a bit more money.
Since higher education is favorable to any nurse, many are returning to school, part-time or full time. There are many programs out there that allows a RN to obtain higher degrees, such as a MSN (master in nursing). RN-BSN, RN-BSN-MSN, BSN-MSN, are just some. I have heard several RN-BSN (also called RN completion program) programs that can be completed in less than a year. Some RN-MSN programs allow RN without a bachelor's degree to obtain a masters (and a B.S.) in two to three years. MSN programs generally fall into two categories -- nurse clinical specialist (I'm not quite sure of the wording on that title) or nurse practitioner. I am not even near there, so I am not quite sure on the difference. Nurse practitioner further breaks down into Peds, Geriatic, etc.. I was told that a NP often makes 60-80 thou a year. You can even get a doctorate in nursing. I'm still working toward my RN degree, so I don't think I am qualified to enlighten you further.

But I hope that helps at least a little. <a href="http://www.discovernursing.com">
www.discovernursing.com</a> is a website made by Johnson and Johnson and it's very helpful.