This is a strange name for a process, but when you know how it affects the cliff face, it is easy to see where the name comes from.
During the day, the heat of the sun makes the rock expand. However, when night comes on and the air cools, the rock shrinks again. The next day, it expands again, and so on. This repeated process results in the cliff face "shedding its skin" like an onion; basically, the outer layer peels of and falls into the sea.
The cliff face is soaked by the rain. It gets into cracks and, on clay cliffs in particular, makes the rock heavier. The rain stops and the cliff face dries. However, the repeated wetting and drying of a cliff face can result in the collapse of part of it, as the heavier rock (e.g. clay) slumps before collapsing.
The rain leaks into the cracks and sits there. As night falls, the temperature falls too, and the rain turns to ice. This means the water expands with the ice crystals. The next day, the ice thaws and becomes water again. If this is repeated, the expanding and shrinking of the water can leave rock crumbling away.
This is caused by plants and animals.
If a rabbit burrows into a cliff near the edge, it can actually cause the rock to crumble. Birds nesting in the cliff face has the same effect.
Also, trees push their roots into the rock and, over time, this causes large clumps of rock to fall away into the sea.
Chemical Weathering (Corrosion/Solution)
This is where the acid in the rain causes a chemical reaction with the minerals in the rock, and the rock erodes away.
This happens more in certain types of rock, such as;