The goal of this weekly game is a technical, but rather non-constraining one. You need to build some new gameplay using C/C++ and SDL (with OpenGL for graphics output). SDL is a mature, open-source, cross-platform (Linux, OSX, BeOS, Solaris, etc.) library that gives you a clean interface to pretty much everything you need to make great games.
Additionally, I highly encourage (but do not require) you to try out nest, which is a slightly cleaned-up version of the code I generally start from when writing game-style stuff in SDL. It provides a streamlined OpenGL context creation process, texture and font handling, slick GL extension loading, a good N-d point class (Vector), and various other niceties.
Please see the page on weekly games for information about how to write an artist's statement and where to turn in your completed game, as well as the standard grading scale.