Person

James the Greater

Son of Zebedee, brother of John the Apostle, Galilean fisherman, and one of the inner three apostles (with Peter and John). The first of the Twelve to be martyred, beheaded by Herod Agrippa I in Jerusalem (Acts 12:2, ~AD 44), and so the only apostle whose death is narrated in the New Testament. Distinguished as "the Greater" to differentiate him from the other Jameses (James son of Alphaeus = the Lesser; James the brother of Jesus). According to a strong medieval tradition, his relics were translated to Compostela in Galicia (northwest Spain), making him the patron saint of Spain (Santiago).

Biographical sketch

Family: son of Zebedee (a Galilean fisherman with hired servants, Mark 1:20, implying a moderately prosperous business); brother of John the Apostle; their mother was likely Salome (cf. Matt 27:56 with Mark 15:40; if Salome was the sister of Mary the mother of Jesus per John 19:25, James would be Jesus's cousin, but this identification is contested).
Calling: called with his brother John from the family fishing business (Matt 4:21-22; Mark 1:19-20). Jesus gave them the nickname Boanērges, "sons of thunder" (Mark 3:17), implying a fiery temperament. Luke 9:54 has the brothers proposing to call fire down from heaven on a Samaritan village, the nickname is consistent with character.
Among the inner three: James, with Peter and John, was admitted to three exclusive events:
Raising of Jairus's daughter (Mark 5:37)
Transfiguration (Matt 17:1-9; Mark 9:2; Luke 9:28)
Gethsemane agony (Matt 26:37; Mark 14:33)
Apostolic lists: Matt 10:2; Mark 3:17; Luke 6:14; Acts 1:13, typically near the top, often second or third after Peter and Andrew.
The Zebedee request (Matt 20:20-28; Mark 10:35-45): James and John (or their mother, depending on Gospel) asked Jesus for the two top positions in the kingdom. Jesus's response, "are you able to drink the cup that I am about to drink?", predicts their participation in His suffering. The other ten apostles were indignant; Jesus used the moment to teach servant-leadership ("not so among you... whoever wishes to become great among you shall be your servant").

Martyrdom

Acts 12:1-2: "Now about that time Herod the king laid hands on some who belonged to the church to mistreat them. And he had James the brother of John put to death with a sword." The dating is tight: Herod Agrippa I died in AD 44 (Acts 12:23; corroborated by Josephus, Antiquities 19.343-350), so James's death must be slightly before that, ~AD 44.

This is the only apostolic martyrdom narrated in the canonical New Testament. Its significance:

First apostolic martyr, the fulfillment of Jesus's prediction (Mark 10:39).
The Twelve as historically endangered: James's death within ~14 years of Pentecost confirms that the early apostles were not living in safety; the resurrection-witness commitment that the apostles maintained was genuinely costly.
Apologetic significance: the would-liars-die-for-what-they-knew-was-a-lie argument for the historicity of the resurrection (see NT Authorship and Eyewitness Apologetics) draws weight from confirmed apostolic martyrdom, of which James the Greater is the clearest-evidenced case.

The Santiago / Spain tradition

The tradition that James preached in Spain before his return to Jerusalem (where he was martyred), and that his relics were later translated back to Spain, develops in two stages:

Mission to Spain: not attested in the New Testament or in the early patristic tradition. First clearly appears in the 7th-8th centuries (Isidore of Seville, the Breviarium Apostolorum).
Translation of relics to Compostela: tradition holds that ~AD 813, during the reign of Alfonso II of Asturias, a hermit named Pelagius was guided by a star to a field (campus stellae → Compostela) where James's body was buried. The basilica of Santiago de Compostela became one of medieval Europe's three great pilgrimage destinations (with Rome and Jerusalem).
Confidence level: the Spain mission is patristic-late and historically thin. Modern scholarship (Catholic and Protestant) generally regards it as legendary; the Santiago de Compostela tradition is liturgically and culturally important without resting on solid early evidence.

Theological themes

Suffering as apostolic mark: Jesus's prophecy that James would drink His cup (Mark 10:39) was fulfilled in martyrdom. The apostolic life is one of bearing-the-cross witness.
Servant-leadership (Mark 10:35-45): the Zebedee-request episode is one of the New Testament's most direct teachings on the inversion of worldly hierarchical ambition in the kingdom of God.
The inner three: James's presence with Peter and John at the Transfiguration places him at the canonical foundation of the Christological revelation, Moses, Elijah, and the apostles together witnessing the glorified Christ.