CodeIgniter is an Application Development Framework - a toolkit - for people who build web sites using PHP. Its goal is to enable you to develop projects much faster than you could if you were writing code from scratch, by providing a rich set of libraries for commonly needed tasks, as well as a simple interface and logical structure to access these libraries. CodeIgniter lets you creatively focus on your project by minimizing the amount of code needed for a given task.
Modular Extensions makes the CodeIgniter PHP framework modular. Modules are groups of independent components, typically model, controller and view, arranged in an application modules sub-directory that can be dropped into other CodeIgniter applications.
HMVC stands for Hierarchical Model View Controller.
Module Controllers can be used as normal Controllers or HMVC Controllers and they can be used as widgets to help you build view partials.