What term describes a nonprotein molecule necessary for enzyme activity?

The term that describes a nonprotein molecule necessary for enzyme activity is "cofactors." Cofactors can be either inorganic molecules, such as metal ions (e.g., zinc, magnesium, iron), or organic molecules sometimes referred to as coenzymes. They bind to the enzyme and play a crucial role in facilitating the enzyme's biochemical reactions by helping to stabilize the enzyme-substrate complex or participating directly in the chemical reaction. For many enzymes, the presence of cofactors is essential for their catalytic activity; without them, the enzyme may be inactive or less efficient.

This contrasts with other terms such as apoenzymes, which refer specifically to the protein component of an enzyme, devoid of its cofactor. Activators imply a broader concept of enhancing enzyme activity but do not specifically denote the nonprotein component required for the functionality of the enzyme. Coenzymes, while closely related, are often a subset of cofactors specifically referring to organic molecules that assist enzymes, but within the context of your question, the more inclusive term is cofactor.