(See also Tar-Anárion, King of Númenor)
Anárion was born Second Age 3219 and slain S.A. 3440 (lived 221 years).
He was the second son of Elendil and the brother of Isildur. His son Meneldil was the last man born in Númenor before the Akallabêth. Together with his father and brother, Anárion was a leader of the Elendilli or Faithful, the part of the Númenórean people that opposed the dark rule of king Ar-Pharazôn and Sauron.
After the downfall Elendil landed in the north near the Elven realm of Lindon, and there established the realm of Arnor, but Isildur and Anárion landed in the south of Middle-earth, establishing the realm of Gondor. Both realms were founded on existing Númenórean colonies: Gondor grew out of the already established city of Pelargir, and the existing Princedom of Belfalas (later renamed Dol Amroth).
Anárion was chiefly responsible for the early ordering of Gondor: he founded the cities of Minas Anor and Minas Ithil, as well as the bridge and city of Osgiliath. Osgiliath was dedicated to the stars, but also after Elendil. Minas Anor and the outlying region of Anórien were named after the Sun, but also after Anárion. Minas Ithil and Ithilien across the river Anduin were named after the Moon, and Isildur.
Gondor was soon attacked by a returned Sauron. In the War of the Last Alliance of Elves and Men Anárion defended Gondor and its people, ruling as its regent, while his brother escaped north to join up with Elendil and the Elves. Defending a land under siege, he successfully defended the Númenórean exiles, the earlier settlers, and the indigenous population of Gondor until Elendil, Isildur and Gil-galad summoned him to take part in the campaign into Mordor. He fought with distinction in the Battle of Dagorlad and in the Siege of Barad-dûr, but was slain in S.A. 3340 by a stone hurled from the Dark Tower. Anárion had four children; the first three were all apparently daughters1, but the fourth child was a son, Meneldil.
Although his line was originally not destined to rule, his son Meneldil became King of Gondor, as Isildur's heirs only ruled over Arnor. Isildur is not recorded as having given up his rights over Gondor, and it appears that the Line of Anárion thus came to rule illegally.
On the other hand, the title 'High King' remained with the northern line, and even as Gondor grew more mighty than Arnor it remained the younger line. The Line of Anárion slowly dwindled and disappeared over time, until in the end the Ruling Stewards denounced the right of any heir of Anárion to ever reclaim the throne, as no one with "pure blood" could be found. This eventually opened the path for Aragorn II to eventually become king of the Reunited Kingdom.
1Although nowhere specifically stated, Anárion's three older children were most likely daughters, as Meneldil received the throne of Gondor. Under the Elendilli the law of cognatic primogeniture apparently did not exist, or an older sister of Meneldil would have earned the crown instead.