Translation:Tomorrow evening, and the evening after
For example, a person might have been asked "When are you going to work on the site for Abrea Corp.?"
Such a time expression ("I am going to make it tomorrow night") requires Accusative. So when a short answer is given, the form required by German grammar remains.
That's why short sentences work so well in such languages: the form of the word often (more or less) hints to the nature of words being omitted.
I'm not sure either but, you can read here that sometimes "Abent" is also "night" http://www.dict.cc/?s=Abend http://dict.tu-chemnitz.de/dings.cgi?lang=en&service=deen&opterrors=0&optpro=0&query=abend&iservice=&comment=&email=