Pompey was a Roman leader who lived from 106 to 48 BCE. He is best known for having been (along with Julius Caesar and Marcus Crassus) one of the men who brought down the Roman Republic and gave rise to the Roman Empire.
These three men were known as the First Triumvirate. The Triumvirate came to utterly dominate Roman politics in their time. Crassus, however, was killed in battle in 53 BCE, leaving only Caesar and Pompey. The two men soon became intense rivals for ultimate power in Rome. Caesar, of course, won the struggle between the two men and Pompey was defeated and later assassinated.
Pompey's main significance, then, was that he participated in the First Triumvirate, which helped move Rome away from a Republican form of government and toward an imperial system.