The Bab (Ali Muhammad Shirazi) was a religious reformer in 19th century Persia or Iran, executed by orders of the imperial government in 1850. The appellation “Bab” means “gate” and is a reference to the Hidden Imam, the Messiah figure of Twelver Shiism, the form of Islam dominant in Iran. His followers, known as Babis, staged several rebellions against the Iranian rulers. After the death of the Bab, his follower Bahaullah claimed to be his legitimate successor and transformed Babism into a new religion known as Bahai, which still exists. Due to extensive missionary activity, Bahai now has branches all over the world. A small faction of traditionalists founded by Subh-i-Azal claims to uphold the original Babi message. Both groups are still illegal in Iran, their native land.
The Bab's voluminous writings have never been translated to English in their entirety, and many have been lost. The Bab's main scripture, his “Quran” so to speak, is known as the Persian Bayan and exists in a 4-volume French translation. This volume, “Selections from the Writings of the Bab”, is published by the Bahai Universal House of Justice. I think it's safe to assume that the selections are pro-Bahai in orientation. The English language is that of the King James Bible, and there are also obvious similarities with the Quran (or perhaps with English renderings of the same!). Like in the Quran, it's not always obvious who is speaking and who is being addressed. The most peculiar writings have been excluded, such as the speculations on the esoteric significance on the number 19. The laws for a future Babi state has also been excluded from this compilation, presumably because Bahai regard them as abrogated by Bahaullah.
The Bab makes far reaching claims on his behalf. He is a prophet on the same level as Adam, Abraham, Moses, Jesus and Muhammad. The Bayan supersedes the Quran. He is also the Qaim and the Mahdi, two titles associated with the Hidden Imam of Twelver Shia Islam. Surprisingly often, he paints himself as divine. Some heterodox Shia groups (such as the Alawites) believe that Imam Ali was divine, in the sense of being a direct manifestation of Allah, rather than a mere man (or a man at all). The Bab's pronouncements are probably to be taken in the same vain. More sensationally, the Bab also talks about a mysterious character called He Whom God Shall Make Manifest. He is said to be even greater than the Bab. At his appearance, even the Bayan will be superseded by new revelations. The Bahais believe that Bahaullah was He Whom God Shall Make Manifest, and that the Bab's prophecies were fulfilled in him and by him.
Another important theme in the translated excerpts is the notion that the Day of Resurrection is allegorical. The appearance of a new prophet and new scripture is “the resurrection”, those who follow him are said to be “in paradise”, while those who reject him are in “the fire”. Revelation is progressive and apparently never-ending. There will therefore be new revelations after He Whom God Shall Make Manifest. Personally, I was mostly struck by the sectarian and Shiite traits in the Bab's message, quite unlike the liberal modernism and universalism of the later Bahai faith (but then, this liberalism is probably mostly for outward show anyway). The Bab's writings contain constant threats of eternal damnation and hellfire (allegorical or not) against those who refuse to accept the new revelation. Even the Bab's own supporters risk judgment if they fail to recognize He Whom God Shall Make Manifest. Occasionally, it sounds as if the Bab himself is this character, but perhaps that simply means he is emphasizing the oneness of all Manifestations of God? The overall context of the message is clearly Shia Muslim.
Interesting if you want to know the real background to the friendly neighborhood cult near you, but probably not for the general reader.