Short answers, pulled from the story.
Jacen Solo is a fictional character in the Star Wars Legends continuity, the son of Han Solo and Leia Organa Solo and the nephew of Luke Skywalker. He is a major character in several novel series, including the New Jedi Order and Legacy of the Force, and eventually becomes the Sith Lord Darth Caedus.
Jacen Solo was created for Timothy Zahn's Thrawn trilogy. He first appeared as one of an unnamed pair of twins in the 1991 novel Heir to the Empire, and was born in the 1993 novel The Last Command, five minutes after his twin sister Jaina, on Coruscant.
Lumiya, the Dark Lady of the Sith, revealed to Jacen in the novel Betrayal that he had already been unknowingly receiving Sith training through Vergere. After killing Jedi Knight Nelani and later Mara Jade Skywalker in the novel Sacrifice, Jacen completed his transformation and chose the Sith name Darth Caedus.
Jaina Solo, his twin sister, defeats and kills Darth Caedus in a lightsaber duel aboard his flagship, the Anakin Solo, in the novel Invincible. She severs his Achilles tendon and stabs him in the heart, ending the Legacy of the Force conflict.
Jacen Solo has been noted as an influence for Kylo Ren, the canonical son of Han Solo and Leia Organa and villain of the Star Wars sequel trilogy. Both characters are the sons of Han and Leia who turn to the dark side, though they exist in separate continuities.
Jacen Syndulla is a canonical Star Wars character introduced by series creator Dave Filoni in the epilogue of the Star Wars Rebels series finale, named in honor of Jacen Solo. He is the son of Kanan Jarrus and Hera Syndulla and was later portrayed by Evan Whitten in the live-action series Ahsoka.