Arrays make it possible to store complicated types of information in a program and manipulate that information. They're ideal for anything that can be arranged in a list and can be accessed easily using the loop statements that you learned about during Hour 8, "Repeating an Action with Loops."
To be honest, the information processing needs of Santa Claus probably have outgrown arrays. There are more children being manufactured each year, and the gifts they want are increasing in complexity and expense. Pokémon alone created a logistical nightmare at the North Pole.
Your programs are likely to use arrays to store information that is unwieldy to work with using variables, even if you're not making any lists or checking them twice.