Something low-key is quiet or understated. A low-key wedding might be held in a friend's backyard, with a potluck reception — it's informal, small, and subdued.
A person who's low-key is modest and soft spoken, and a low-key restaurant is comfortable and unpretentious. You might prefer your family's low-key way of celebrating birthdays (a cake and a few gifts) to the way your best friend's family does it (hiring caterers, clowns, magicians, and a band). Low-key can also mean "muted in color," like the low-key tones in your favorite painting.