Я не понимаю. =I don't understand. Я не знаю.= I don't know.

I will just correct the pronunciation: Ya ni panimayu. Я не понимаю. You can say that, when you don't know the meaning of what someone is telling you, or the language that they speak e.g I don't understand Chinese. Я не понимаю китайский язык. I'm sorry, I don't understand you. Can you explain that again? Ya ni znayu. Я не знаю. You say that : 1)when you don't have information about smth, e.g.I don't know the right answer. Я не знаю правильный ответ. 2) when you aren't sure about smth e.g. What are you going to do this evening?-I don't know yet. Я ещё не знаю.(because you haven't made your mind up yet ) 3) when you aren't familiar with a person, place etc: e.g. I don't know him. Я не знаю его.

Natalya is right. For example - you can know, but don't understand. Like rules of grammar) or - "я понимаю твои чувства, но не знаю, что их вызвало". I understand your feelings (I see that you are happy, sad etc - but I don't know what coused it.