Aburage (sometimes spelled abura-age or abure-age) is thinly sliced deep fried tofu, crisp and brown on the outside and white and soft on the inside. These tofu pieces can be carefully slit and opened to make pockets into which sushi rice is inserted to make inari sushi. They can also be added to other vegetarian dishes for extra flavour and protein.
Aburage can be bought canned or frozen in Asian markets; in this form, run it under very hot water to remove excess oil before using.
You can also make it yourself from firm tofu. First, drain excess moisture from the tofu by placing a cutting board on top of it and letting it sit for a few hours. Then, cut the tofu into thin triangles about 2 inches/5 cm a side and half as thick. (If the sliced tofu is thicker, you're actually making asuage or atsuage.)
Heat oil in a wok. Traditionally, aburage is deep fried, but you can shallow fry it too; you just need enough oil so that when it bubbles it reaches most of the way up the side of the tofu. Heat your oil until a chopstick dipped in bubbles (see how to deep fry for tips). Carefully slide the tofu into the oil and fry till golden brown on both sides, flipping once. Remove to paper towels to drain, and to achieve a really nice crispy texture and good colour, cool and fry a second time, then drain and cool again. Finally, place the aburage in a colander and run under very hot water to remove excess oil, then pat dry. They'll keep for up to a week in the fridge.
(Ouroboros dips his tofu in flour to soak up excess oil before he fries it. You could try dipping it in cornstarch too, I guess. But this is not traditional.)