Step 1: Understanding the Concept
Activated charcoal has a very large, porous surface.
Step 2: What happens
On shaking, methylene blue molecules collect and stay only on the surface of the charcoal. They do not spread through its bulk.
Step 3: Result
Accumulation of a substance at a surface, rather than in the interior, is adsorption. This removes the dye and the solution becomes colourless.
Final Answer:
The phenomenon is adsorption.
\[ \boxed{\text{(C) }\text{Adsorption}} \]