What does nonobvious mean in terms of patentability?

This is the question that has no definitive answer. The patent office is not supposed to use "impermissible hindsight" which renders almost all inventions obvious. This is the kind of thing that happens when you see an good answer to a problem and think to yourself - "Why didn't I think of that?" That would be an example of impermissible hindsight. Of course getting to the "right" kind of obviousness is the patent office's job. It is difficult to say exactly what is permissible and what is not. The letter of the law is written so that if it would be obvious to one skilled in the art of whatever your invention is - the so-called PHOSITA - (person having ordinary skill in the art) then you are not entitled to a patent. If your invention would be deemed obvious to a person skilled in the field of knowledge related to your invention, then it is not patentable but if would take experimentation, etc. to come up with your solution, then it should be patentable. It is anything but clear and that is the way it is with most things in the law. You have the black letter and then you have to decide the individual case based on the particulars. Since most patents are for improvements over things that already exist (very few patents are for brand new areas of invention) the answer to the question of what is obvious is a tough problem and one that no patent professional can answer with absolute surety.

Obvious or not obvious - that is the question. To be patentable your invention must be (1) new, (2) useful, and (3) not obvious to persons have ordinary skill in the field of the invention. Patent attorneys fight obviousness rejections issued by the patent examiner on a daily basis for their clients. How different is you invention from the prior art? A small difference - is more likely to be an obvious change. A large difference - is more likely to be not obvious. Many inventions fall in the middle - so we fight about obviousness. The Supreme Court case known as "KSR" goes into detail about how to study this issue. It has a Wikipedia page. GOOD LUCK!

It means that a person having ordinary skill in the art would not have known to do what is claimed, based on all of the prior art in existence before the earliest priority date of the application.