Qualitative Variable:
A qualitative variable also known as a categorical variable is one which is not capable of taking numerical measurements. An observation is made when an individual is allocated to one of several mutually exclusive categories. Observations falling in each class can only be counted. 
For example sex(either male or female), general knowledge(poor, moderate, good), and color(blue, green, red, etc).

Quantitative Variable:
A quantitative variable is one which is capable of assuming a numerical value. 
For example the height of plants, the weight of grains, or the number of students in a class.

Context