A patch is a modification to vanilla NetHack not created by the DevTeam. Hundreds of patches can be found at the Bilious Patch Database. Historically, a small handful of popular patches have been incorporated into official releases.
If you want to know how to patch your NetHack sources, see the article on patching.
patch is also a program that can apply specially formed patch (also known as "diff" after the program that creates them) files. The usual invocation of patch is along the lines of
patch -p1 < patch_file
patch for the Windows platform may be downloaded from http://gnuwin32.sourceforge.net/ (though it seems to have problems under Vista). After downloading, the patch.exe file needs to be placed in the system PATH, so that it can be found when it is invoked from the command line. One possible place would be in the same directory as the compiler used to compile NetHack (e.g. \mingw\bin) for the MinGW compiler).