As we note in our article on ancient Christian symbols, which we recommend for further reading:
What did the fish represent? Above all, it was Jesus Christ. The dominant language of the early Church was Greek, and in Greek the phrase “Jesus Christ, Son of God, Savior” produced the acronym ICHTHYS, the Greek word for fish. A Christian poem of the second century spells the word with the first letters of each line. Thus, the fish is a simple creed: It professes belief in Jesus’ divinity and his identity as the Christ, the anointed Savior (see Matt. 16:16).