The first several text lines at Cygwin's web site seem clear to me:

" Cygwin is a Linux-like environment for Windows. It consists of two
" parts: A DLL (cygwin1.dll) which acts as a Linux API emulation layer
" providing substantial Linux API functionality.

That means it's a DLL under Windows that mimics a UNIX/Linux system.

" A collection of tools which provide Linux look and feel.

That's all the GNU software and other stuff you get using apt-get.
I haven't yet found any programs over the 10+ years I've used Cygwin
that wouldn't work under Cygwin but, as they wrote, you must recompile
and link from the source code. No big deal:

$ ./configure
$ make
$ make install

for most anything worth using that isn't already part of the Cygwin
repos. I typically grab everything from the repos -- only 1+GB or so.

" The Cygwin DLL currently works with all recent, commercially
" released x86 32 bit and 64 bit versions of Windows, with the
" exception of Windows CE.

That means it works on Win95, Win98, WinNT, WinXP, WinVista, and even
Server 2003 and Server 2008 using any 32-bit or 64-bit single, dual,
or quad core/CPU system (essentially everything available) and what
doesn't work with UNIX/Linux/Cygwin (e.g., Windows programs :-) still
works under Windows.