Wikipedia's page is currently more complete than this page. The goal here is to explain, eventually, some events and design decisions (without needing to cite everything). You can see the overall project activity throughout the years on Ohloh.
PiTiVi was started in 2004 as an "end of studies" project by Edward Hervey and his classmates at the French computer engineering school Epitech. The "PiTiVi" name came from the combination of "Epitech" and "TV".
In 2005-2007, development stalled due to various factors, including the fact that Edward (the only active PiTiVi developer at that time) was hired by Fluendo to work on GStreamer. Improving GStreamer was necessary in order for PiTiVi to be usable, but this meant that PiTiVi did not get as much direct development attention. During that time, PiTiVi was also rewritten in Python (it was initially written in C). A more detailed explanation can be read in this blog post by Edward in 2007.
In early 2008, it was decided that PiTiVi had outgrown its original design specifications and needed to be re-architected. The result was the 2008 Architectural Redesign. In late 2008/early 2009, it was announced that Collabora Multimedia would invest developer time in improving PiTiVi (and hire additional developers to accelerate its pace). The results of Collabora's help on that front were dramatic, as can be seen in the significant amount of commits in 2009-2010.
In late 2009/early 2010, the GES library was created to address many architectural problems around non-linear editing with GStreamer. Starting in 2011, efforts on the PiTiVi side have been focused on porting to GES, cleaning and stabilizing the whole stack (PiTiVi, GES, GNonLin, GStreamer and related technologies like GObject introspection) while fixing longstanding bugs and adding new features.
As part of a website and branding facelift in 2013, the traditionally camel-cased "PiTiVi" name was changed to simply "Pitivi".
To this day, the project lives on, thanks to the continued efforts of many dedicated people.