The CO2 reacts with the limewater to form a milky solution. This is due to the formation of Calcium carbonate which is not very soluble in water.
The equation for the reaction is:
Ca(OH)2 + CO2 ----> CaCO3 + H2O
I'm also correcting my answer: after a long period of time the solution will become clear due to the formation of the more soluble calcium bicarbonate.