The T3 framework is a Joomla templating framework that was originally developed by the team at Joomlart. It was created in the days of Joomla 1.5 when rapid development of the CMS was non existent and new features and functionality were desired but weren't available.
Since they found themselves reusing code over and over again it made sense to reuse the code and add it into a base framework that they could build upon for each one of their template releases.
This idea wasn’t just appealing to template clubs but also appealing to many web design and development studios/agencies around the world including us at PB Web Development. Many of these studios were producing solutions for clients everyday but finding that they were in the same situation of using the same code over and over again on various different websites.
There were many base templates out there already, such as 960 grids or even the free templates that came with Joomla that could have been used as a base template framework but people wanted more than what these could provide. Hence the more complex template club frameworks.