What is the difference between a quantitative and a qualitative measurement?

Quantitative data is numerical. (Quantities) This type of data results from measurements. Some examples of quantitative data would be:

the mass of a cylinder of aluminum was 14.23g the length of the pencil was 9.18cm

Qualitative data is non-numerical. (Qualities) Some examples of qualitative data would be:

-the color of the sulfur sample was yellow -the reaction produced a white solid -the object felt soft -the reaction produced a strong ammonia odor

Very good examples and nice pictures can be found here: http://regentsprep.org/regents/math/algebra/ad1/qualquant.htm