A Roman Centurion was the equivalent, more or less, of a non-commissioned officer in American military today. Typically promoted from the ranks, a centurion would normally have charge of 100 men (a “century”), though the actual number could be somewhat flexible depending on circumstances.
As there were no Roman legions stationed in the land of Palestine during the time of Jesus, the two centurions that appear in the Gospels would have held slightly different roles. Jesus’ healing of the centurion’s servant in Matthew 8 (Luke 7) took place in the territory of Herod Antipas, who was permitted to maintain his own military forces, so it is likely he was in the pay of Herod rather than the Romans. The centurion who was over the crucifixion of Jesus would have had been over some of the auxiliary troops under the control of Pilate, the Roman governor of Judea.