Note that cygwin is two things.
A directory tree mimicing a unix file system with /var /usr /home.

A dll file that all cygwin applications gets linked with. This dll file contains an almust full set of API simulating a Unix system (including translation between '/' and '\' in paths.

So to the Windows system, a Cygwin program is a normal Windows application. But the source code is almost standard Unix code built with a Cygwin-adapted version of gcc.

Early on, it was just an environment for command-line tools, but Cygwin has now been extended to also handle graphical applications by looking like X. Early you got a X desktop where the graphical Cygwin applications run but now the Cygwin applications may look and behave like a standard graphical Windows application making it almost impossible to notice that Cygwin has been involved.

The emulation is good enough that a very large percentage of applications available for Linux, BSD or other similar can be reasonably simply ported to Cygwin. In many cases without any source code modification at all.

And it is possible to run Cygwin applications without the user installing Cygwin on the computer. As long as the application doesn't has special requirements for other programs/files it can be run stand-alone as long as it is distributed with the cygwin dll.

The GNU implementation of AWK (gawk) has probably been available from just a couple of days after the initial start of the Cygwin existence. awk, lex, yacc, make etc are part of the basic build environment for a unix system.