Here are some common paper traits and their definitions, courtesy of Mohawk Papers.
Opacity: This measures the amount of light passing through a sheet of paper in values from 1 (the most transparent) to 100% (the most opaque). A paper with high opacity will have minimal show through to the other side. If your project has large solids and heavy coverage, a sheet with a high opacity is important.
Brightness: This is measured as a percentage of light reflected from the surface of the paper. It is not necessarily related to whiteness or color. A paper with a brightness of 98 is a very bright sheet with almost all the light being reflected back to the viewer. Full color printing images appear to pop on bright white papers as they illuminate transparent printing inks.
Finish/smoothness: This affects ink receptivity and ink holdout. Smoothness is measured on the Sheffield scale. A higher value on the scale usually indicates a rougher sheet.
Environmental Qualities: Many clients now request the use of recycled paper or paper manufactured with renewable energy. There are many more recycled papers available today along with better quality papers.
Formation: This refers to the distribution and uniformity of the fibers in a sheet of paper. A badly formed sheet will show more dot gain and a mottled appearance when printed. A quality formation will exhibit ink absorbing equally so solids look smooth.