What it is: a library facilitating complex TUIs on modern terminal emulators, supporting vivid colors, multimedia, threads, and Unicode to the maximum degree possible. Things can be done with Notcurses that simply can't be done with NCURSES. It is furthermore fast as shit. What it is not: a source-compatible X/Open Curses implementation, nor a replacement for NCURSES on existing systems.
for more information, see dankwiki and the man pages. in addition, there is Doxygen output. there is a mailing list which can be reached via email@example.com. i wrote a coherent guidebook, which is available for free download (or paperback purchase).
i've not yet added many documented examples, but src/poc/ and src/pocpp/ contain many small C and C++ programs respectively. notcurses-demo covers most of the functionality of Notcurses.
Notcurses abandons the X/Open Curses API bundled as part of the Single UNIX Specification. For some necessary background, consult Thomas E. Dickey's superb and authoritative NCURSES FAQ. As such, Notcurses is not a drop-in Curses replacement.