Just as a flame tossed by the force of wind
Quickly goes to its cessation and subjects not itself to any designation,
So the sage released from the mass of names
Quickly goes to his cessation and subjects not himself to any designation.
(—from the Questions of the Brahmin Student Upasīva, Sn 1074)
It may be that most people in America, if they hear the word "Nirvana," are more likely to associate it with a grunge rock band from my old home town of Aberdeen, WA than with the Buddhist Absolute. Even most American Buddhists may be more likely to associate the word with a hypothetical, expanded yet nevertheless still worldly, psychological state than with a mystery that is totally Off The Scale. And it may be that most Asian Buddhists are more likely to identify Nirvana/Nibbāna with an eternal, blissful place not located on this planet, like a perfect heaven realm. I once lived at a large monastery in Myanmar where a poor woman used to come and sweep the grounds in exchange for merit, plus probably some of the monks' leftovers from lunch. One of the monks joked with her, saying that as a result of her meritorious acts she would attain Nibbāna; and she replied that she didn't want to go there, as there are no tea shops in Nibbāna. Fair enough, I guess.
Since the subject of this article is Nirvana, I may as well begin with a discussion of the name itself. Both the English word "Nirvana" and the Pali word "Nibbāna" are derived from the Vedic Sanskrit word Nirvāṇa, which most philologists nowadays agree literally means "blowing out," as in the going out of a fire. This has been somewhat controversial, as the commentarial tradition, which makes its own rules for etymologies, claims that Nibbāna comes from ni-, which means "without," and vana, meaning "desire" or "attachment" (and incidentally having the same Indo-European origin as the Latin name Venus). A modern monastic author has attempted to vindicate this derivation of the word by putting forth a case that it really means "unbinding," based on ancient Indian notions about the nature of fire. Fire to the ancient Indians had a bound state and an unbound one, and through combustion the fire bound in the fuel was set free.
However, it would seem that in order for this derivation to be valid, the word would have had to have this meaning originally; and it would seem that in Indo-European languages in general there is an idiom of outwardness with regard to the dying of a fire. For example in English we say that it "goes out," even though we don't suppose that it actually goes anywhere. In Latin the word is extinguere, which means "to quench out"; in German, I've been told, to extinguish a fire is called auslöschen, with the aus- meaning "out"; and in Slovenian it's izginiti, with the iz- also meaning "out." It would be interesting to see what the word is in a language more closely related to Sanskrit, like ancient Persian; but overall it seems that the prehistoric Proto-Indo-Europeans already had an idiom of going or doing something outwards, away from the present place, for a dying fire, and it would seem risky to assume that they also had metaphysical ideas about fire lying latent and bound in unburnt wood. Furthermore, the verb form of the Pali word nibbāna is obviously nibbāyati, from ni-, "out," and vāyati, "to blow." So Nirvana literally means, in all probability, the blowing out or dying of a fire—in this case the fire of attraction, aversion, and delusion.
There are a whole slew of synonyms for it in the texts, both in Theravada and Mahayana, which need not be listed here. I will mention, though, that one of my favorites is nippapañca, which literally means "non-diversification," and might loosely be interpreted as nonduality, which is certainly one way of interpreting the Absolute. But enough with mere names.
It is said in Theravada Buddhist books that there are two kinds of Nirvana/Nibbāna, that of an enlightened being before he/she dies, and the kind afterwards. This is similar to another splitting of Nirvana into a metaphysical state (the Absolute) and an ethical one (the realization of that Absolute). But ultimately Nirvana cannot be divided into different kinds. There is a maximum of one kind. It's all the same.
One uncontroversially attributed quality of Nirvana is that it is unconditioned, asaṅkhata. This has some rather odd implications which often remain unconsidered, but which are fun to consider if one likes to have one's mind warped.
For example, if Nirvana is unconditioned, then it is clearly not the result of a cause. This is very difficult for some traditional Buddhists to accept, as they consider Dharma a means of arriving at Nirvana; and if Nirvana is not the result of a cause, then all one's practice will never result in enlightenment. Practice is doing; and doing is karma; and karma leads to conditioned results and more karma, not to Nirvana. The Zen Buddhists seem more prepared to appreciate this; as is said in the Platform Sutra of Hui Neng, "Ultimately, there is neither attainment nor realization; how much less sitting in meditation!"
Also, if Nirvana is unconditioned, then it would have no boundaries in space or in time, as a boundary would be the result of a cause or causes. No conditions, no limits. Thus Nirvana has no beginning and no end. If it is to be found in the mind of a Buddha, it is also to be found in the mind of a serial killer, and in a penguin, and in a brick. And if it has no beginning or location in time, it could hardly be called a cessation of suffering, or of greed, hate, and delusion, or of anything else. Some Theravadin texts have tried to argue that a cessation is not an event, and so can be unconditioned; but still a cessation has a beginning, and presumably also an end, since whatever has a beginning naturally tends to have an end. And if it thus has limits in time, it is conditioned, and not really Nirvana. This also has been appreciated more by Mahayanist philosophers than by Theravadins; for instance the Mahaprajnaparamita Shastra says, "The sambodhi par excellence is devoid of any obtainer, devoid of any place or time of obtaining."
It seems to me that orthodox Theravada is in shackles when it comes to understanding Nirvana/Nibbāna. The Abhidhamma philosophy declares that Nibbāna is one of 82 ultimate realities, no more ultimately real than, say, earth element, odor, femininity, right livelihood, or wrong view. But if it truly is unconditioned, which idea is uncontroversial in itself, then it would have no boundaries in any respect, and thus could not exclude any of those other 81 supposed realities, or be fundamentally differentiated from them. If it is anywhere at all, it would be everywhere, and, in a sense, everything.
But by the very same token, because it has no boundaries or determinate content, it would also be, in a sense, nothing at all. In fact Nirvana, being an unconditioned Absolute, totally transcends duality, and can have no opposite, because having an opposite would imply a boundary, a limitation. It is not the opposite of Samsara. Thus Nirvana, like God also in some theologies, is so completely unconditioned that it cannot be said to exist or not to exist. It is totally Off The Scale.
This may be acceptable, more or less, to philosophically-minded Buddhists; but it leads to a stickier point: if Nirvana cannot be said to exist or not to exist, then enlightened beings also cannot be said to exist or not to exist. Enlightenment itself becomes unavoidably problematic. In fact a medieval Indian school of Buddhism, the Yogacara Logicians (also called the Dignāga school), commonly used as an example of a problematic premise, i.e. a statement that could not possibly be known as true or false, the statement that "Enlightened beings exist." From a samsaric point of view there is only Samsara, and all conceivable points of view are samsaric.
Yet even so, still more paradoxically, when Dharma stops emphasizing enlightenment in this very life as its primary purpose, it stops being genuine Dharma and essentially dies, or becomes comatose at the very least.
If all of this has confused you, that's good, because if we think we understand Nirvana, we really don't.