Double cleansing is fundamentally cleaning your skin twice.
This is to be done at the end of the day, just a single cleanse for the morning.
The first cleanse is best done with a Pre Cleanser, as these are designed to remove as much of the initial dirt, debris, oil and make up.
The second cleanser is helps to remove the final residue and cleanse the pores effectively.
Double cleansing can also be done with the same product used in the second cleanse.
There are different types of cleansers available, foaming( be careful of these as many can just strip the skin of the natural oil) , purifying, cream, wash, granular, exfoliation
PS> The photograph shows Eve Taylor Cleansing brushes. These help the effectiveness of the cleanser whilst also improving the blood circulation and lymph drainage of the face.