When a raw, shell-less egg was placed in sugar solution, the egg shrank. The egg was brought back to its original size by placing it in water. Which process does the experiment demonstrate?

The process that the experiment in question demonstrates is called Osmosis. It is the process in which a solvent moves from a region of higher concentration to a region of lower concentration through a semi permeable membrane. This way the concentration of the solution in both sides of the membrane becomes equal.