What was the Xbox 360's online marketplace called?

The Xbox 360's online marketplace was called Xbox Live Marketplace.

Microsoft used Xbox Live Marketplace to distribute downloadable games, game expansions, themes, videos, and other digital content for the Xbox 360. The service operated through Xbox Live, the console's online platform, and used Microsoft Points for many purchases during much of the Xbox 360 era.

Microsoft later moved toward direct local-currency pricing and folded the marketplace experience into the broader Xbox Store. The original Xbox also supported Xbox Live, but Xbox Live Marketplace became especially important on Xbox 360 because downloadable content and digital games expanded substantially during that generation.