Now you know how to remove the egg peel without breaking it. The peel of the egg is made off calcium carbonate and the vinegar is a diluted solution of acetic acid. In the present experiment, the acetic acid reacts with the carbonate of calcium contained in the peel of the egg, producing carbon dioxide. The reaction is faster in the initial instants because the reagents are in maxim concentration.
In the end of the experiment, the egg without peel stays stable. That is due to the existence of a surface membrane that doesn't react with the vinegar. However, this membrane has the capacity to allow the migration of the vinegar from out to in of the egg. The fact that the egg is larger in the end of the experiment is due to the migration of vinegar to the interior of the egg. In other words, we are in the presence of a natural selective membrane. Now that you already understood this experiment, you already know how to remove the egg clothes without breaking it. With science, the impossible becomes possible! Try it and enjoy science!