Short answers, pulled from the story.
Upādāna means clinging, attachment, or grasping in Buddhist thought, though its literal translation from Sanskrit and Pali is "fuel." It is considered one of the two primary causes of dukkha, or suffering, alongside taṇhā, which means craving.
The Buddha, in the Sutta Pitaka, identifies four types of clinging: sense-pleasure clinging (kāmupādāna), view clinging (diṭṭhupādāna), rites-and-rituals clinging (sīlabbatupādāna), and self-doctrine clinging (attavādupādāna). According to Buddhaghosa, these are ordered from most obvious to most subtle.
Buddhaghosa distinguished the two using a thief metaphor: craving is stretching out one's hand in the dark toward an object not yet reached, while clinging is grasping the object once reached. Together he called them "the roots of the suffering due to seeking and guarding."
The Fire Sermon, known as the Āditta-pariyāya and recorded at SN 35.28, is a teaching in which the Buddha tells the bhikkhus that everything, meaning the five senses, the mind, and all operations and feelings they produce, is burning with the fires of greed, hatred, and delusion. Upādāna, meaning fuel, is the ninth link in the chain of Dependent Origination and the substance that keeps this burning going.
Nibbāna, the Pali form of nirvana, literally means to "go out" or to blow out the flames of defilement. In the context of the fire metaphor embedded in upādāna, liberation is understood as what happens when clinging stops supplying fuel to the burning mind.
In Hindu texts, upādāna typically means "material cause" or "substrate." The medieval Vaishnavism scholar Ramanuja used the compound upadana-karana to describe Brahman, understood as Vishnu, as the material cause of the universe. Realist schools such as Samkhya and Nyaya also used the term to describe Brahman as the substrate of the phenomenal world.