It's kind of along the lines of saying "however". or even "but". I haven't finished doing my book report, nevertheless I must hand it in tomorrow. I haven't finished doing my book report, but I must hand it in tomorrow.

Nevertheless means in spite of that . EG : I'm feeling ill ,but I shall come with you nevertheless .

www.thefreedictionary.com/nevertheless

However- although- even though- in spite of.

так говорят когда перед этим сомневались чем либо. например: "все-таки она мне нравится"