Nevuah is a
Hebrew term meaning, approximately,
Prophecy. According to most commentators, when used in
Tanakh, the
Talmud, and other Jewish works, it is a specific type of communication that is via an indirect channel from G-d. This can be in the form of "visions" (See the opening verses of Yeshayahu) or instructions, with the ability of the prophet to respond.
Prophecy, in
jewish literature, is something that theoretically anyone at a high enough level, who has purified themselves and acheived knowledge of the nature of G-d, can attain. Realistically, prophecy at this level was supposed to have ceased during the second temple period, not to recur until the
Messiah arrives.
According to the Rambam's philosophical treatise, Moreh Nevuchim (Guide for the Perplexed, Book 2, Section 45), there are eleven levels of Nevuah.
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The first level is that of a "helper of G-d," such as the Judges (from the book of Judges) and King David. This is also the level that Moses had when he killed the Egyptian Slavemaster. (Exodus 2, 12)
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The second level is that of someone who speaks for G-d, to deliver rebuke, explain G-d's wisdom, etc. People on this level include Solomon, Ester, and Daniel (of lion's den fame.)
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The third level is that of dream revelation, where the prophet talks to G-d. This is the level that Proverbs was written based on.
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The fourth level is that of clearing a voice of G-d clearly in a dream. This is the level Samuel had when he first had a prophecy.
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The fifth level is speaking with a "man" in a dream, who is an emmisary of G-d's.
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The sixth level is speaking with an Angel in a dream. This is the level of most prophets.
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The seventh level is a dream in which a concept that G-d sends is received by the prophet.
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The eighth level is a dream in which an allegory is imparted. Some of Abraham's prophecies fall into this category.
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The ninth level is hearing words in a waking vision from G-d.
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The tenth level is speaking with a "man" sent by G-d as a messenger, such as the vision Joshua at Jerico.
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The eleventh level is speaking with an Angel sent by G-d while awake.
Comparatively, there are other levels of "Prophecy" that would not properly be called Nevuah, including both the lower level of Ruach Hakodesh and the higher level of Moses, who was able to talk "face-to-face" with G-d, a level which no other person has, or will, ever attain. (The Rambam's 13 Principles of Faith) All other levels are lower than this, such as the level of the Tannaim, who composed the Talmud, who were at the level were they merited to hear a "Bas Kol," or Heavenly Voice. To get some sense of what this entails, the level of being able to raise the dead, according to the Talmud in Tractate Avodah Zarah, is before that of Ruach HaKodesh, and Nevuah is even greater than that. The Talmud also states that (normal) dreams are one sixtieth (a fraction frequently meaning a small part) of Nevuah, meaning that there is some message there, though not in the same way as actual Prophecy.
At the time of the first temple, the Talmud states that there were twice as many prophets as there were Jews who left Egypt, with academies of them existing. The books of "Prophets" that are currently extant in the form of the books of the Old Testament (excepting the 5 Books of Moses, which was transcribed directly according to G-d's explicit direction) were written with Nevuah, though they contain only those prophecies that are germane to the future needs of the Jewish Nation, and certainly not all of the prophecies given. This is abundantly clear from the fact that many times prophets whose prophecies do not survive were consulted at various times in the stories of the Prophets.
According to many Jewish sources, the epic of Ester marks the end of Nevuah, and the beginning of a new era, in which the Jewish Nation is able to understand what it is that we are intended to do purely based on what has been previously revealed using only our intelligence, making the challenge of the Diaspora a very different on than previous ones, where the answers were clear, if uncomfortable.
There are several important things to note about Orthodox Judaism's view of Nevuah as opposed to that of other religions. The Chumash is very explicit about what a false prophet is, including anybody who prophecies that any part of the Torah is false or no longer applies, or anybody who attempts to change the Halacha as it currently stands. A person who did such a thing, during the time of the Temple, would be put to death. In addition, a prophet is not accepted unless they are known not only as a person whose actions put them above all rebuke, but also is known as someone who has mastered all parts of Judaic knowledge.
None of this is personal opinion, it is all very well grounded in various works of classic judaic scholars. (From the Talmud, to pre-15th century Scholars.) If you would like to know what the source for any particular Jewish beleif is, I can probably track it down, and it is only not sourced here because of the variety of sources most of the concepts come from.