Virtualization, from virtual (machine).
When you want to test run an Android app, you can either use an Android device connected to your computer (which is the recommended way), or use the Android emulator that comes with the SDK.
The emulator is agonizingly slow, and the only way to make it faster is to use an Intel CPU that supports virtualization, install haxm and set up the virtual android device to use an Intel image (instead of an ARM one). That way the emulator can use hardware accelerated virtualization, which is significantly faster than emulating the entire Android system with just software.
So if you do have an Android phone or tablet, you don't need to worry about virtualization or haxm. Just activate its developer mode and connect it, and Android Studio will offer you to run the app on it.
(To be clear: Android studio does not _require_ hardware virtualization, it will run perfectly fine without it.)