Nirvana is the state or realm of truthfulness, acceptance, bliss, awareness. Nirvana has a self-sustaining quality to it, that it's somehow more whole, holistic, fully integrated. The term "sukka" is sometimes used to describe the perception of nirvana, meaning "good fit" (contrast to dukka above). Here we also see fruition of a Non-Dual perspective of the world. The world is one, all things are one, together somehow. Rather than seeing the world as still in this "oneness" kind of way, think of it as always moving and dynamic; the world if a continuum, and in that continuum they are all one. No underlying "power", just a constantly shifting dogpile of forces that affect everything else. From the personal side about this view point, Nirvana is about total awareness; you, as an individual, are clear of your distortions when perceiving reality and thus become a kind of cosmic mirror that only reflects truthfully what is.
I mentioned Vajrayana before too and how Samsara and Nirvana are the same. This also re-examines the notion of Karma. Rather than seeing karma as a kind of fate or causal network that pulls you along, a vajrayana buddhist seeing karma as more the principles of causality and causality that are always at work and unescapeable. To be at all means to deal with, work with, become one with karma. Samsara is a repeating cycle or causal patterns; Nirvana is about breaking out of patterns and being acausal. Do you see how these could both work together? There's no "out there" and no "in here"; trying to overcome nonduality. In that sense, having a conception of what Nirvana is could be a big hurtle to cross.
Zen: Speaking of concepts that are hard to understand, Zen. Another thing that makes it hard is that Zen has almost no theology, metaphysical description, whatnot, about it. Zen so much wants to get out of patterns, it's often very surreal and absurd their methods. Confusion, non-conceptuality are the most promissing, Nirvanic states for them... leave everything behind, ideas and habits, and just expereince. In fact, Zen has an added term to how enlightment (or an enlightened view) is reached: Satori, which is an enlightenment expereince. Stories about it often describe disciples trying very hard to achieve a zen mind with their masters being seemingly dickheads about it and asking very odd things of then, only to have the disciple have a satori experience while sweeping the floor or tasting tea or getting a smack on the head. A Zen buddhist does a type of meditation called Zazen, or sitting meditation. It's kind of like a Samatha that sometimes employs the use of mudras and mantras (hand gestures and repeated expressions).
Manjushri: was an Indian sage from early on... I can't remember when right now, probably 2nd to 5th century sometime. He's was known for his incredible intellect and discernment; thus, when Manjushri is supplicated in chants or whatever, it's to say stuff like "oh Manjushri let us mentally cut through matter to see the subtle impermanence of things". Awareness and Focus are sometimes contrasted when dealing with concentration (Samadhi). They are actually opposite: awareness wants to include and broaden, and focus wants to lessen and take away and become specialized upon and target fewer things. Manjushri is more about focus here. Others, like descriptions of the bodhissatva with 1000 eyes, are about awareness. Just like figures in other religions, because they lived so long ago and from the mythologizing of their deeds and lives, they are told to be super-humans semi-enlightened or enlightened beings.
3 Vehicles: Okay, a brief run down of the three vehicles, or really viewpoints, in Buddhism. It should be noted within each vehicles are still many contrasting views and slighting hairs between the various schools. Also, these schools do not "progress" from worst to best; they're all interconnected and serve different roles, though Vajrayana is the most recent by time.
> Theravada or Hinayana ("lesser vehicle"): deals with the causal, cosmological aspects of buddhisms. It can be the most dogmatic but also the most scientific and ontologically questioning. Concepts like the 12 nidanas (chain of dependant origination) or Karma or the 10 Bhumis one progresses through to reach enlightenment or taking on precepts are all iconify Hinayana style. It's called "lesser vehicle" in constrast to "greater vehicle" to show that it can help one individual become fully realized in relation to their own perspective towards reality, but not be able to skillfully aid others or their enlightenment (self-realizers).
> Mahayana ("greater vehicle"): all about compassion, openness, acting selflessly, acting to put others ahead of yourself. Concepts like Sunyata, different types of compassion, or perspectives involving many people at once are Mahayana. "Greater vehicle" refers to the fact that you want to get enlightened so that you can help others get enlightened, kind of hold the door open before deciding not to return to physical incarnations.
> Vajrayana ("adamantine vehicle"): Takes the rules, throw em out the window. Everything is possible means, possible energy to propel you towards enlightenment. We there's no good or bad so let's do everything we can right now to act enlightened and be our true selves. Contains concepts like Skillful means, or (as I said in my first post) Enlightened Society, and is much more prone to work with emotion, desire, mental events and view them in sometimes anthropomorphic ways (similar to hinduism with it's variable polytheism).
Proof of Enlightening? Is it all just mental with no other effects? Well, from the buddhist perspective, everything is mind. The world does not, in a way, exist; only a pluralism of perceptions. Changing your mind IS changing everything. Jeez, I just realized I haven't described the 4 Noble Truths (like a medical diagnosis of suffering):
1) There is Suffering. I think these all have a single word name too, and this one is Samsara.
2) There is a Cause of Suffering. Karma
3) There is an End of Suffering. Nirvana.
4) There is a Cause to an End of Suffering. Dharma, which is teaching that aid enlightenment. This term actually has many possible definitions, and Hinduism again uses it too, but in a Buddhism sense it just means enlightening teachings.
Some Bodhisatva are said to be able to do funky things like fly or teleport or create duplicate images of themselves or other such fancy things. But that possibly isn't true and most certainly is not the point of this. Actually, there's a term for a being that goes through the enlightening processes but retains or inflates their ego: a Rudra. Just as a Buddha is enlightened but egoless, a Rudra is a big, smart, selfish, egoful mother fucker.
In buddhist cosmology, there are six worlds of beings: animals, hungry ghosts, angry gods, humans, happy gods, and maybe the other one is insects. Each has their own strength and own probable weakness. As a Vajrayanist myself, I see them as more psychological states; angry could just be a drug dealer, animal could be an actual animal or some ignorant hick. It's kind of important that there is a supposed realm above humans so we don't get too high and mighty about ourselves. The flaw of the happy god realm is that they are really wise but they actually think that, because they are so wise and may know about emptiness, they "are" something. Humans are considered to have the ebst shot at enlightenment, with their flaw being desire with discipline as the possible remedy.
You know what I'd say the proof is? Getting some degree of happiness in your less, letting go of crap that is just not you, not getting all pie-in-the-sky about actually being good right here right now. Having a steadiness that lets you ride through anything with an openness that lets you still be in the moment and unclinging to the past. If you become a dogmatic buddhist, might as well call yourself a monotheist... theism or atheism is not the point. Those terms deal with an "out there" or nothing "out there" quality; but why, why is that needed? See the world and let yourself just be.