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Prophet Daniel (pbuh) is of the prophets who haven’t been named in the Quran, nevertheless, there are many hadiths that speak of him.
According to most of the hadiths, he lived during the reign of the oppressive king of Babylonia, Bakhtul-Nasr who would bother and harm him. As several historical sources assert, Bakhtul-Nasr was defeated and overthrown by Cyrus the Great of the Persian empire. In a tafsir we read: “One of the most famous cities that (Cyrus) conquered was the city of Babylonia which was conquered in 538 b.c. and after that, he ordered for the return of the Jews to their homeland after 70 years of captivity and exile, and also allocated plenty of wealth from the treasury to the rebuilding of Babylonia; at that time, Daniel (pbuh) was in the court of Cyrus.”
Keeping in mind these points, it can be said that Prophet Daniel (pbuh) lived 2500-2600 years ago. Of course there are also other historical hadiths that say he lived after Prophet Yahya (pbuh), which means about 2000 years ago. The apparent contradiction between these two groups of hadiths can be solved by saying that considering the fact that during that time some prophets such as Prophet Nuh (pbuh) lived for hundreds of years, Prophet Daniel (pbuh) could also be one of them, thus both sets of hadiths are correct.
As for who his parents were, just like many other prophets and historic personalities whom historians and those recording history didn’t care much about who their parents were because of its insignificancy to them, one can't reach a certain conclusion on it; but what is for sure is that he is one of Bani Israel’s prophets and of the descendants of Prophet Yaqub (pbuh).
Anyway, although this prophet isn't famous like others such as Nuh, Ibrahim, Musa, Isa (peace and blessings of Allah (swt) be upon all of them), nevertheless his distinguished fame in Iran might be because of the grave that is said to be his in one of Iran’s cities by the name of “Shush of Daniel” (Shushe Danyal) that has been named after him. Another thing he might be famous for are the many occasions and victories and defeats that Bani Israel underwent during his time that have been mentioned in detail in tafsir and hadith sources.
 See: Muhammad Baqir Majlisi, Biharul-Anwar, vol. 14, pg. 351.
 Seyyid Abdul-Hujjat Balaghi, Hujjatul-Tafasir wa Balaghul-Iksir, vol. 1, pg. 204, quoted from Ketabe Danyal, vol. 6, pg. 28.
 Muhammad Baqir Majlisi, Biharul-Anwar, vol. 15, pg. 355.
 For instance, see: Seyyid Ne’matullah, Qisasul-Anbiya, pg. 426.