A "hard science" is a field of scientific study which involves precise measurements of observations and well-defined methods for obtaining and interpreting new knowledge.
Chemistry, mathematics, and physics are definitely hard sciences. Astronomy and natural sciences like biology and geology also are usually thought of as hard sciences (though it depends on the eye of the beholder; to someone like a hard-nosed analytical chemist, other disciplines like ecology may seen hopelessly soft). Psychology, sociology, anthropology, and other social sciences are considered "soft sciences." But as their bodies of knowledge build and research techniques become more refined, the "soft" sciences get harder.
Part of this writeup is based on work I did for the science dictionary at http://biotech.icmb.utexas.edu/