A wheel is a zip file that can be interpreted as a python library; it contains the file layout as it should be installed in on the destination machine.
Wheels can include binary executables; until recently, there was no standard way to target linux, so win32 & osx installations for certain python libraries were way faster. The manylinux project makes it possible to distribute binaries for most linux distros by linking against common versions of shared libraries.
With luck this will replace distro-specific packages (i.e. apt-get, yum, apk) for python libraries with large compiled binaries. That's good for users ('pip install' works for more cases) and for package maintainers (less customization to support).
Wheels are Python packages, not unlike Ruby gems. They can optionally include shared libraries which extend Python with native code. This appears to be an attempt to standardize how such libraries are compiled for Linux.
Looks like arch users will need to install at least one package from the AUR(ncurses5). But apart from that, I'm pretty excited for this, it should make stuff like installing pyqt5 in a virtualenv really simple.