A more thorough explanation:

The explanatory-phrase rule is a principle in trademark law that states that if a company uses a family name as a trademark and another company uses the same family name for competing goods or services, the senior user of the family-name trademark is entitled to a judicial remedy for unfair competition. This remedy requires the junior user to include an explanation on their signs, labels, and advertisements that they are not affiliated with the senior user's company.

This rule is based on two conflicting principles: (1) everyone has the right to use a family name in business, and (2) no one may use a family name in a way that unfairly hurts someone else's business.

For example, if a company named "Smith & Sons" sells shoes and another company also named "Smith & Sons" starts selling shoes, the senior user of the trademark (the original "Smith & Sons" company) can take legal action against the junior user for unfair competition. The junior user would then be required to include an explanation on their signs, labels, and advertisements that they are not affiliated with the senior user's company.

This rule helps to protect the reputation and goodwill of the senior user's company and prevents confusion among consumers who may think that the junior user's products are associated with the senior user's company.