The Ushahidi v2.x web application is written in the php programming language, using the Kohana 2.3.1 framework over a SQL (currently MySQL) database (Note that SwiftRiver is built on Kohana 3.2).

Kohana is a Model-View-Controller (MVC) framework, where a framework is like a structure that you can build your code on, that handles lots of otherwise time-consuming things like making all your pages have a similar look-and-feel. MVC gets its name because it splits application code into Model, View and Controller files.  Simply put (there are some complications to this, but not enough to change the basic explanation), Model files contain code that describes the data structures being used by the application;  View files contain code that tell the framework how to display information to the user;  and controller files contain code that converts system inputs (e.g. you clicking a mouse or data coming into a feed) into actions. 

If you look at the Ushahidi github repository, you'll see a directory (application) with subdirectories labelled Models, Views, Controllers and a couple of other things important to Kohana applications (like hooks and libraries).  Hooks are important because they're pieces of code used to trigger additional actions (like you displaying an extra message on your Ushahidi pages).  Other application subdirectories include libraries, i18n (translations of Ushahidi phrases across languages), logs, cache, config and helpers.