First wave is the nineteenth-early twentieth century movement that brought about voting rights and more legal emancipation for women. Very basically, it was more about laws. And, for whatever reason, temperance.

Second Wave was the mid-late twentieth century movement that focused on the idea of "Women's roles" in society. This would be sexual roles, career roles, the whole works. There were laws involved (Roe vs Wade for example), but it was much less about the legal status and much more about the broader place women had in western society.

Third Wave feminism is a little tricky because it is quite a bit broader. Some of it has to do with expanding western views on gender into other cultures, and some of it is more of a continuation of second wave feminism in the sense things like pay differences. It also has expanded into transgenderism and the like. On top of it, particularly in the English speaking world, is the popularity of "Privilege theory" in Sociology and the movement to produce policy based on it. That is where things get controversial. Whereas Privilege theory itself isn't completely off base, it is incredibly easy to oversimplify, and since it is popular with the college-going white middle class, people who get into Privilege theory tend to slight the importance of economic factors in favor of those things that apply to them.

And radical feminists are those who went off the deep end and want to start castrating dudes. We should start investing in codpieces soon...