Hammerspoon is a tool for powerful automation of OS X. At its core, it is just a bridge between the operating system and a Lua scripting engine.
This is very hard to describe succinctly. You can write Lua code that interacts with OS X APIs for applications, windows, mouse pointers, filesystem objects, audio devices, batteries, screens, low-level keyboard/mouse events, clipboards, location services, wifi, and more.
Typically you would write a configuration file in Lua that connects events to actions. You might want to bind a keyboard shortcut to a series of window operations, or an applescript. You might want to run a series of commands when your wifi interface connects to your home network. You might want to display an alert when your battery drops below a certain percentage. You might want to do something crazy like have iTunes automatically start playing when your Mac detects you are in Paris.
If you want to explore the options Hammerspoon offers, check out the Getting Started Guide and the full API documentation.