Babylon was probably a symbolic name for Rome. Like Rome, Babylon was a great city and the capital of a large empire. In the 500s BC, Babylon ruled much of the ancient Near East.
Babylon was also the empire that burned Jerusalem and took many Israelites to live in Babylon as captives. Because of this history, many Jews saw Babylon as the center of a world that opposed God’s people. For this reason, the book of Revelation uses Babylon as a metaphor for Rome, or as a code word that pointed to Rome. Peter probably used the name in the same way.
Mark, also called John Mark, was another co-worker of the apostle Paul. He wrote the Gospel of Mark, which many people believe is based on Peter’s teachings.