The 'eternal now' has two meanings in the world of writing, one referring to an acceptable narrative practice, and one distinctly pejorative.
The most common usage refers to a narrative that does not advance the characters along the time line despite the theoretical passage of a significant amount of time. A good example of this is The Simpsons, in which none of the characters age at all, despite periodic birthdays, major holidays, and other clear markers of passing time.
As a term of criticism, the 'eternal now' is used to describe a work that ignores the supposed period of a story to present certain aspects of the narrative in the modern day; the most famous example of this is perhaps the striking clock in Julius Caesar. Shakespeare certainly had good reasons for including it, but the Romans did not yet have this technology. While these sorts of anachronisms were common in Medieval art and Tudor plays, it is nowadays consigned to weaker works of amateur writing, and was first labeled by Robert M. Schroeck in reference to common errors in fanfic.