I saw this on a luggage tag at O’Hare airport.

Problem:
An apostrophe appears where it should not.

Explanation:
An apostrophe should not be used to pluralize a family name. The brightly colored luggage tag was meant to call the reader’s attention to the fact that the luggage belonged to the Nelson family.

Use of the definite article on the luggage tag told me that the family name was Nelson.

The plural of Nelson is Nelsons (not Nelson’s). For example, The Nelsons live in suburban Chicago.

If the luggage-tag writer had wanted to indicate that the luggage belonged to the Nelsons, then he could have written The Nelsons’. Note the possessive apostrophe after the pluralized family name.

Solution:
“The Nelsons”