The short answer is that under the high-temperature conditions of the boiling water or steam, the polyphenol oxidase enzyme is denatured. Most likely your instructor wants you to give an explanation of what denaturation is, how it occurs, and how it relates to enzyme structure and function.
Biological enzymes such as polyphenol oxidase are proteins—long chains of amino acids joined together by peptide bonds. There are a variety of different amino acids that differ in their R groups. The important thing about these differences is that some are polar, meaning that they have one atom with a slight positive charge and another with a slight negative charge. The chain of amino acids is somewhat flexible and tends to settle into an arrangement where a positive part of one amino acid is near a negative part of another. This arrangement is known as a “configuration,” and protein configurations are generally stable (meaning that they don't change) at room temperature.
The configuration of a protein is important because the “chain” of amino acids is wrapped and condensed into a three-dimensional shape. This shape is essential to a protein’s function. In the case of an enzyme, the shape brings reactants in a chemical reaction together in an orientation that allows the reaction to occur at biological temperatures (many reactions would only occur at much higher temperatures—unsuitable for life—in the absence of enzymes).
The shape of a functional enzyme, however, is only one of many possible configurations that a particular amino acid chain could potentially adopt. Proteins fold as they emerge from ribosomes during synthesis, taking on their one and only possible configuration that is actually functional. If the configuration of an enzyme were disrupted, without breaking any chemical bonds, the chance that it would return to its functional configuration, instead of some other random configuration, would be infinitesimal.
This is what denaturation is. Heating the enzyme causes the atoms in it to vibrate and move, and the energy and motion can overcome the electrostatic attractions between different R groups. We envision the amino acid chain flopping around. When cooled, it settles into one of the millions of possible configurations available to it—but not into the functional configuration. It no longer has the shape needed to promote the oxidation reaction that produces the brown color, so browning does not occur.