"Any time now" means that you don't know the exact time, but that you expect it to happen very soon; momentarily. An equivalent expression might be:
"Some time soon, Nana will show up with the cookies."
It looks as if this expression is mainly used in American English, and any time now (see 12) may more often be written with "any time" as two words. Note that "anytime" is an alternative and you may see the similar expression anytime soon written with "anytime" as one word.
There does not seem to be a strong convention about when to write "any time now" as one or two words. "Any time now" appears in COCA 73 times; "anytime now" in COCA, 24; when looking at categories such as fiction, "any time now" is still the winner, but the difference is negligible. The corpus is most useful for understanding how "any time now" is used in this sense - it often has a connotation of impatient waiting (like hoping for the cookies to arrive soon), or a sense of anticipation, not always pleasant:
She looked at her watch. "The kids should be home any time now."
The captain almost fired me tonight. I'm on my way out. Anytime now.