The term Freebase client refers to the website at http://freebase.com/ Obviously it is not the only Freebase client out there, but it was the first major one, and so tends to be referred to as "the client" by Freebase staff.
Parts of the Freebase client
The original client was written by Python and is closed source. However, it is the officially stated to plan to move the entire client into Acre, with the consequence that it will be open source. As of September 2010, some parts of the client (for example, the front page and the query editor) are in Acre, but the main topic view/edit page is still in Python.
Firefox, Safari and IE (versions?) are officially supported for the website. Opera is not supported, but much of the site will work OK in it.
The new release of the Freebase client is almost ready to launch.