There are two basic factors that affect how a certain clay works to cleanse and remove impurities from the skin, its Cation-Exchange Capacity (CEC) and sorptive properties.
Cation Exchange Capacity, abbreviated CEC, measures the number of cations (positively charged ions) that can be retained on the negative surface of the clay and then can be exchanged with other positive ions (cations) when dissolved in a water-based solution.
The theory is that since clay is made largely of minerals, these positively charged good minerals are then able to exchange with positively charged impurities in the surrounding area which are removed from your face as part of the clay, thus leaving good natural minerals behind on your skin.
Sorptive properties describe the process by which one substance becomes attached to another.