It means something that has a sharp/acidic/bitter taste. It is astringently sour. A lemon is a good example! It also means having a bitter and sharp manner. Examples:.
…'Twain was renowned for his acerbic wit.' .
'Twenty years later, Arlen's book is still one of the biggest inspirational best-sellers of all time, but the man has devolved into a bitter recluse whose acerbic utterances, such as "Hell is other people," send all those who cross his path running for the hills.' -SFGate, San Francisco Chronicle website, July 24, 2009. [See Related links below for news source] ( Full Answer )