Wine, also known as Wine Is Not an Emulator, is an ultra-popular compatibility layer for UNIX-like operating systems which allows users to run unaltered Windows programs with ease. Its use is especially popular within the Linux community, however, macOS is also a system which often takes advantage of the layer.
The compatibility layer has now reached version 3.0 which includes native support for Android. This sounds great, however, keep in mind that Wind is not an emulator, just as the name says. Running x86-compiled desktop programs won't work on an Android device which is powered by the common ARM SoC. In order to take full advantage of the Wine compatibility layer, you'll need an x86-powered Android device, which includes some older Asus phones, a big chunk of Chromebooks and some tablets.
This may be disheartening, however, seeing how demanded Wine is by many, it's most likely just a matter of time before eager developers develop an underlying emulator which would allow Wine to execute binaries compiled for different architectures, however, how practical that would be is still unknown. The official Wine project has also stated that Wine will use a fork of QEMU in order to emulate the processor instructions, however, that fork isn't finished yet.
As the overwhelming majority of Android phones out there are ARM-powered, Wine cannot run most Windows programs, however, Windows RT, Microsoft's failed attempt at an ARM device, does indeed run many ARM-compiled programs and developers have compiled many popular open-source tools for the architecture which can now be run on ARM Android devices. Some of the applications include 7-zip, Notepad++, Quake and many more. A list can be found over at the XDA Developers forums