The 2006 Nobel Prize in Physics goes to John C. Mather and George F. Smoot "for their discovery of the blackbody form and anisotropy of the cosmic microwave background radiation".
The award honours the achievements of the COBE (COsmic Background Explorer) mission, which was the first to measure the anisotropies in the cosmic microwave background radiation (for the discovery of which Penzias and Wilson were awarded the 1978 Nobel Prize). The cosmic microwave background (CMB for short) is the light emitted by the gas in the young (about 300,000 years after the Big Bang) universe when it had cooled down far enough for atoms to form (to about 3000 Kelvin), making it transparent for light for the first time. The expansion of the universe since then has caused the light emitted then to shift its wavelength to the microwave range by today (about 14,000,000,000 years after the Big Bang), causing it to look like that of a black body of temperature 2.728 Kelvin. In fact, one of the achievements honoured by the award is the demonstration that the measured CMB spectrum is the best fit to a perfect blackbody spectrum ever seen. The other achievement being honoured is the measurement of the tiny anisotropies in that background which were caused by density fluctuations in the primordial gas, which later would form galaxies and stars through gravitational collapse. This work has had a huge impact on our understanding of the early history of the universe. A more detailed study of the CMB is being done by WMAP, which also has made huge contributions to our understanding of the history and composition of the universe (so who knows, maybe there will be another Nobel Prize for CMB explorers in the future).
More about this from Backreaction, Dave Bacon, Cosmic Variance, Clifford Johnson, Andrew Jaffe, Rob Knop, Chad Orzel, Steinn Sigurðsson or the conventional media.