chouchin 提灯

In Japanese, chouchin 提灯 means "paper lantern," because it's a lantern made out of paper, also known as "Chinese lantern," because often you'll see it as the iconic red one.

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Meaning

The word chouchin 提灯 means a "light," hi 灯, that you can "take with [you] in [your] hand," te ni sageru 手に提げる. In other words: a portable light, a lantern.

A tobidashi bouya 飛び出し坊や holding a "paper lantern," chouchin 提灯, which reads Tenmaya 天満屋.

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A boy-shaped sign holding a paper lantern on hand.
- tobidashi bouya
  飛び出し坊や
  "Boy jumping out." Imagery used in many traffic signs around Japan.
- Tenmaya
  天満屋
  The name of a character in the anime.

Note that the word doesn't actually have anything to do with paper. It just happens that they're traditionally made out of paper.

More specifically, a flexible material, typically bamboo, is turned into thin strips and bent into rings. Those rings are stacked vertically with some space between them, and that's going to be the frame of the lantern. Then, paper is glued on those bamboo rings.

The horizontal lines you see on paper lanterns are those bamboo rings. Since the rest of it is made out of paper, it can contract and expand vertically, like a spring, or an accordion

For reference, a video showing how they're made:

It's worth noting that despite its name, nowadays people don't go around with such "lanterns" on hand. Instead, they're mostly used to decorate places and in festivals.

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Decorative paper lanterns shaped like squids.

A way you may see them being actually held in hand would be in reference to guards from the Edo period, which are often shown carrying around such lanterns in their patrols.