In the USA (unlike a lot of places internationally) law is a post-bachelors endeavor (i.e. you apply to law school after you finish your traditional 4 year college degree). Some people apply their senior year fall and go to law school right after college while some others choose to apply when they have already graduated and have had some time working (perhaps working in government or for a law firm as a paralegal or even doing management/strategy consulting).

And, yes, you are totally right - you do not need a specific undergraduate degree to get in!