Clay sensitivity refers to the degree to which a clay soil will undergo a reduction in undrained shear strength as it undergoes any disturbance that causes remoulding / volume change. The higher the sensitivity, the greater the loss of strength.
For a good explanation of this (although somewhat old now) view the paper by Mitchell and Houston (1970)
Mitchell J.K. and Houston W.N. (1970) Causes of Clay Sensitivity. Journal of the Soil Mechanics and Foundations Division, Proceedings of the American Society of Civil Engineers. Vol. 95, pp. 845-871.