Draw two curved lines like this:
What do people see? A fish.
The first Christians had enemies among Jews and Romans, government and citizens. It was not always safe for Christians to identify themselves. So the Christians adopted a symbol as their code--the fish.
In the first century, the fish was a more common symbol than the cross. A cross was used to kill people; a fish was used to feed people. It didn't arouse suspicion. (What would happen if you walked into an airport with a gun pendant hanging around your neck?)
Fish showed up a lot with Jesus. He called fishermen to follow him as learners (disciples) and later named them emissaries (apostles). According to Luke, Jesus first gave them a miraculous catch of fish (Luke 5:1-11). Jesus fed 5,000 men with five little fish and two loaves. After he rose from the dead, he provided another miraculous catch, and cooked some fish for his tired followers (John 21:1-14). As a symbol, the fish reminds us of Jesus.
As a word, fish tells us who Jesus is. It's an acrostic: the first letter of each word is a word. ("scuba" means "self-contained underwater breathing apparatus".)
Ask a Greek speaker what this says in English:
He'll say "It says 'fish'. It's a fish that says 'fish'."
Ἰησοῦς ihAYsoos JesusSo "fish" in Greek stands for "Jesus Christ, God's son, Savior"
Χριστός khrisTOS Christ
θεου THEHoo God's (or "of God")
υἱός hweeOS son
σωτήρ sohTAYR savior