A portion of the IEEE POSIX standard which provides a consistent C programming interface to many Unix operating systems. Microsoft claims that Windows NT is POSIX compliant, but the implementation is generally considered to be crippled at best, since otherwise Microsoft would be unable to lock people into their proprietary APIs.
Recently (2001, basically), the POSIX.1 standard merged with the Single Unix Specification (SUS). It is now much larger and more complete (aka more bloated).
POSIX, at least pre-POSIX-2000 POSIX, did not standardize a lot of things that people commonly used, the most important of which was the BSD network sockets API.
POSIX.1b is the POSIX realtime extensions, and POSIX.1c is the POSIX threads specification. There are other POSIX standards, some of which are standard, some in progress, and some dead. One of the more interesting is POSIX.1e, which provided a capability API for Unix. It is now dead, but the draft API is supported by some systems, including Linux.