For such an important character, almost nothing is known of Eldarion's life or deeds. Almost the only definite statement about him came from his father, who commented that he was 'full-ripe for kingship' in The Tale of Aragorn and Arwen (given in Appendix A I (v) to The Lord of the Rings). Aragorn's ancestors had tended to take over their duties as Chieftain at about the age of ninety: if Eldarion followed this pattern, this would place his birth in the years around IV 30.
Eldarion inherited his Kingdom in a manner that recalled the ancient traditions of Númenor: his father Aragorn Elessar gave him the tokens of his rule, and then gave up his life willingly, as his mighty ancestors had done thousands of years before. The new King's mother Arwen left him to rule alone, passing away to the now-empty land of Lórien, where her long life also came to an end. As well as being the Heir of Isildur and High King, his descent from Elrond through Arwen made Eldarion the lord of the remaining Elf-lands of Middle-earth. This fact seems to be the source of his name, which apparently means 'Descendant of the Eldar'.
What these great titles meant in practice, cannot now be known. There are references in the History of Middle-earth that make it all but certain that he left descendants to rule after him, but apart from these, no details of Eldarion's time as High King are recorded.