Artamir was a dunadan and prince of Gondor. He was the son of King Ondoher.
Artamir marched to the Black Gate of Morranon with his father, the King. Unknown to both them and most of the army was that Artamir's brother, Faramir I, was at that battle too. It was against Gondor's customs for a king and all his sons (if he had more than one) to march into battle (for fear of the king and the son(s) dying and leaving Gondor without a king). Unfortunately, Ondoher, Artamir, and Faramir all perished in the Battle north of Morranon with the Wainriders.
Gondor was without a king and so Arvedui tried to make a claim to unify The North and South Kingdoms. This was rejected and Gondor was led by a Stewardship until the King returned at the end of the third age.
Little did the Wainrider who slew Artamir know that he was the reason Gondor and Arnor were reunified one-thousand years later. Had he not, Aragorn would have come to Minas Tirith to find a King, which would have prevented him from becoming King himself. That would also have prevented him from marrying Arwen Undomiel, who was not permitted, by Elrond, to marry a human any less than the King of Gondor and Arnor, which would result in the ending of the first line of the Chieftains of the Dunedain.