"Japanese lantern" is one of the common names of the Physalis alkekengi plant. Another common name for this plant is the "Chinese lantern." Like the potato, Physalis alkekengi is a member of the nightshade family.
According to the Missouri Botanical Garden, the fruit of the plant is edible, but is tasteless and not typically used in culinary applications. The paper-like pods of the Japanese lantern skeletonize, creating a dramatic lantern-like appearance that lends to its name. SFGate recommends growing the plants in moist, well-drained soil in an area that gets full sunlight and removing the dried out pods from the plant and growing bed to prevent it from self-seeding.