The third Noble Truth is dukkhanirodha i.e., dukkha can cease (nirodha). If one does not hanker after anything and if he has no desire left in him, he does not suffer and dukkha ends. To know that suffering can come to an end is just called ñāṇa (knowledge). But to know and experience that it can cease to be is kicca ñāṇa. When one has realized that dukkha (suffering) has ended, i.e., there is no more of it, it is called kata ñāṇa. This is knowing the third Noble Truth completely in all its three aspects.
Dukkhanirodha is nothing but nibbāna (nirvāṇa in Sanskrit). This is the summum bonum of human life according to the Buddha. When the root of dukkha is eliminated, suffering in life and continuity of life, i.e., being born again and again in the cycle of birth and death, stops forever. This state is called the state of desirelessness (taṇhākkhaya) which is characterized by complete extinction of desire.
What this state of nibbāna is cannot be answered adequately and perfectly in human language, which is not capable of describing experiences beyond our sense organs. It is here that the limitation of language becomes obvious. However, there are terms, though negative, which attempt to describe it. Taṇhākkhaya (extinction of desire), asaṅkhata (unconditioned), nirodha (cessation), virāga (non-attachment) and nibbāna (extinction) are such terms. From these terms at least one gets an idea that nibbāna is the absence of desire, extinction of desire and non-attachment to the various objects, viewpoints and dhammas of the world. In the Saṃyutta Nikāya the Buddha himself has defined it as ‘the complete cessation of that very taṇhā, giving it up, renouncing it, emancipation from it, detachment from it.’ (Yo tassāyeva taṇhāya asesavirāganirodho cāgo, paṭinissaggo, mutti, anālayo 3.484.)
In the same Nikāya (1.162.), it has been defined as ‘Sabbasaṅkhārasamatho sabbūpadhi paṭinissaggo taṇhākhayo virāgo, nirodho, nibbānaṃ’, i.e., ‘calming of all conditioned things, giving up of all defilements, extinction of all “thirst”, detachment, cessation, nibbāna’. In the same Nikāya (2.24), Sariputta defines it as rāgakkhayo (extirpation of desire), dosakkhayo (extinction of aversion) and mohakkhayo (extinction of ignorance). (Yo imesu pañcasu upādānakkhandhesu chandarāgavinayo, chandarāgappahānā so dukkhanirodhoti.)
In the Mahāhatthipadopama Sutta, Sāriputta pithily defines nibbāna as the destruction of desire and craving for the five aggregates of attachment. (Yo imesu pañcasu upādānakkhandhesu chandarāgavinayo, chandarāgappahānā so dukkhanirodhoti. Majjhima Nikāya 1.252) Musila, one of the disciples of the Buddha, says that bhavanirodha (cessation of continuity and becoming) is nibbāna. (Bhavanirodho nibbānanti -- Nidāna Saṃyutta Kosambi Sutta 1.102). In short, it is a state where one ceases to burn from the three fires of craving, aversion and ignorance.
The Buddha identifies nibbāna with truth (Taṃ saccaṃ yaṃ amosadhammaṃ nibbānaṃ -- Majjhima Nikāya 3.294)
One important point should be considered here. When one says that taṇhākkhaya is dukkhanirodha; does it mean that the extinction of taṇhā is the cause of nibbāna? The answer is an emphatic ‘No’. Nibbāna is not produced or caused. It is not saṅkhata (produced). It is asaṅkhata (unproduced).
Walpola Rahula gives an apt simile to bring this point home to us. ‘There is a path leading to the realization of Nirvāṇa. But Nirvāṇa is not the result of this path. You may get to the mountain along a path, but the mountain is not the result, not an effect of the path. You may see a light, but the light is not the result of your eyesight.’
What I have detailed in the topic titled “Nibbāna” should be added here because nibbāna is nothing but dukkhanirodha.