This (CYGnus pseudo-uNIX) is a project to run Linux applications on windows. Concept here is same as in case of BSD and Linux emulation with only different that here cygwin1.dll as APi for linux emulation and there's a collection of tools. In latest release windows 2000 , XP ,vista and 7 are supported.
Many major applications of linux you see are compiled on it like Open Office , Sun Java.
But if you ever need an application of linux on windows which is no available you can use cygwin to compile it using gcc ( yes you can use it on windows using it).
It supports for open gl and X. Also applications that run on 64 bit arch are under wow64 not as 64 bit.
It is a dual license project much like MySQl one as Open Source and another closed source for those wanting to make proprietary softwares. It is under Red hat Inc.
This is a must have thing for people trying to port application to windows.