Looking at the corrected graphcorrected graph in Michael's answer, showing both git-core and git on Debian systems, the question seems to be why git started to become popular in 2006 on Debian systems and why it grew exponentially between 2006-2012.
The reason could be the strong adoption of Debian-based Linux distributions, like Ubuntu, which started to become popular around 2005-2006 and became the #1 distro up until around 2011, when Mint, also Debian-based, became #1. In the end of 2012, Mint is still #1 and Ubuntu #3 according to DistroWatch.
GitHub, founded in 2008, provided free git hosting, and between 2008 and 2012 became the #1 source repository service in the world with ~2.5 million users and ~4.5 million projects, according to Wikipedia in late 2012.
Rails and many other projects switched from Rubyforge to GitHub in the late 2000s. In addition, Bundler was introduced around the time originally in question (late 2009) with support for installing/updating gems via a :git option in the Gemfile, and Bundler was included as a dependency of Rails 3. Projects in Python, Javascript, C, C++, Java, CSS, etc. also migrated to or started on GitHub.
Those that wanted to contribute to the projects on GitHub needed to fork the project in GitHub, use a local git client to clone the repository before making amendments and pushing them back into GitHub and doing a pull request. This was much simpler than other methods used before and arguably was a significant reason that it was adopted by the projects that moved to GitHub or decided to start there. This meant git-core/git needed to be installed in the Debian-based distros so that developers could use GitHub.
So, I believe that it was a combination of Debian-based distros becoming more popular and growing git adoption because of GitHub's growth in users and projects, which likely stems from GitHub's free hosting and user experience.