The Japanese deep-fried tofu pouch often used in kitsune udon is aburaage.
Aburaage is made by slicing tofu thinly and deep-frying it, creating a light, airy piece that can be opened into a pouch. It readily absorbs flavorful liquids, so cooks often simmer it in soy sauce, mirin, sugar, or dashi before serving.
In kitsune udon, the seasoned tofu rests on top of udon noodles in broth. The dish’s name refers to foxes, or kitsune, which Japanese folklore associates with a fondness for fried tofu. Aburaage is also used to wrap sushi rice in inarizushi. A thicker fried-tofu product is called atsuage, while agedashi tofu is a separate dish of fried tofu served with savory broth and toppings.
Tofu skin, or yuba, is a different soybean product formed from the skin that develops on heated soy milk. It may resemble aburaage in some preparations, but it is not the pouch traditionally meant in this question.