Advanced Placement Exams are a suite of standardized tests created by the College Board, the same entity that administers the SAT and related tests. There are currently 34 of them, ranging from Art History to Environmental Science to Microeconomics to three flavors of Physics.
High school students are generally given a limited opportunity to take AP Classes. If you're in a good school and get good grades, you might get the chance to take as many as six by your senior year. However, if you're able to pay a small fee, you can take any of these tests at the end of any school year. Any school that administers AP Exams is required (I think) to allow you to take them, regardless of whether you've taken the course or are even enrolled in the school, and you can probably find a school within a few hours that offers any given exam. Colleges will treat a high score on the test the same whether or not you've taken the formal course.
When applying to a college, if your academic transcript contains, say, twelve passed AP Exams, it will look twice as impressive as that of a high-school valedictorian. You'll have proven in a very direct and comprehensible way that you are good at academics, that you have taken initiative, and that you are willing to work within the system to appear remarkable. You'll get into more colleges and get more merit-based scholarship offers.
Furthermore, you'll have an advantage in negotiating the college bureaucracy once you're in. Some colleges will let you apply all of your AP exams directly as course credit, which means you can enter as a sophomore if you have enough. This not only shortens the time necessary to get your degree, but gets you access to the advanced classes with high-quality professors faster. Most will at least let you use some of your tests in lieu of some of the general education requirements: e.g. if you've gotten a 4+ score on both Spanish Language and Spanish Literature, you probably never have to study a language again if you don't want to.
To figure out whether this will work for you, go to the College Board's Teacher's Guide site. For each subject that even vaguely interests you, download an old test or a practice exam (you may need to identify yourself as a teacher when creating a login account; this is never a lie). You may find that you are already qualified to take several exams, and nearly qualified for many others! This despite your school (if you have one) claiming that you need to wait three more years and sit through nine months of classroom instruction first.
- Make sure you schedule your exams well in advance. Schools can change the deadline for registration at any time, and they can't warn you if they don't know who you are.
- You don't need to "teach to the test" when engaging in self-study. One method is to take a quick look at the curriculum at the beginning of the year, check one or two of the recommended books out of a library, then follow your own bliss. A month or so before the test, take a practice test, and if necessary do some cramming on the bits you've missed. An afternoon or three with a teacher or professional in the subject can be useful in filling in the gaps, especially with regard to jargon.
- <EDIT>Per the comments, don't bite on this bullet point; its claims are overconfident.</EDIT> If you're a voracious reader of fiction and a decent test-taker, you can walk into the English Language and English Literature exams with no preparation and get a perfect score. I don't know of any others that don't require at least a little prep--you can be a self-taught expert in a subject and still not know the College Board-approved jargon.
- In written essays, be warned: there are slightly silly quantity-over-quality grading guidelines. Know them ahead of time. Almost every essay requires two or three independent arguments or examples. It's much better to have two bad arguments than one good one. You'll often want to go in having a few different "case studies" that you know the details of.