Crucifixion was a method of execution practiced on Earth by a number of different civilizations beginning in the 7th century B.C.E. Crucifixion was practiced by among others the Greek, Persian, and Assyrian cultures on Earth. The Romans were perhaps the most notable culture to employ crucifixion as a means to execute criminals.
Crucifixion was a particularly brutal, painful, and gruesome way to execute a person. The Romans considered crucifixion an extremely dishonorable way to die, and used it those they considered to be the worst criminals. A person who was crucified was tied or nailed to a cross - a wooden beam attached to another wooden beam anchored into the ground. The person would eventually die from exposure and shock. (TNG novel: Spartacus)
The ancient rebel leader Spartacus was crucified by the Romans, along with a large number of his followers after leading an unsuccessful slave uprising against the Roman state. While Lt. Commander Data and a visitor from the Vemla fleet to the USS Enterprise-D were viewing a holodeck recreation of the uprising, one of the characters encountered mentioned the Romans would have them crucified if they lost. Data explained the practice to the visitor. (TNG novel: Spartacus)
Perhaps the most notable figure crucified by the Romans was the human religious leader Jesus Christ, whose teachings were the cornerstone of the Christian religion on Earth. In the centuries following the crucifixion of Christ the cross would become the symbol of Christianity. Some branches of Christianity, such as the Roman Catholic branch would often display a cross with a physical representation of the corpus, or body of Christ attached. Such a object was referred to as a crucifix. In the Leonardo da Vinci holodeck program that Captain Janeway had been particpating in, there was a crucifix on one of the walls of da Vinci's workshop. (VOY episode: "The Omega Directive")