To be more accurate there are multiple levels of POSIX compliance and the actual certification for POSIX compliance costs a pretty penny. The boring details are here
http://www.opengroup.org/onlinepubs/009695399/toc.htm , but basically it just defines a unix like view of the world for programs so that the programmer can make som assumptions about the system.
With unix services for windows (MS SFU) on either windows 2000 or XP, you can get have access to most POSIX features on the windows platform.