When you're away from home and you miss it terribly, you're homesick. Most kids get homesick when they first go to summer camp.
Everyone feels homesick sometimes, but it's probably most common for kids to get homesick when they're on their first sleepover or visiting their grandparents, or even when they leave for college as freshmen. There is a wistful yearning included in the idea of being homesick — a longing to be back where you started. Homesickness came first, from the German heimweh, "home woe" or "home pain."