The acronym means "Jesus, Christ, Son of God, Savior". The Greek letters break down as follows:
I - Iota is the first letter of Iesous (Jesus)
X - Chi is the first letter of Christos (Christ)
Θ - Theta is the first letter of Theos (God)
Y - Upsilon is the first letter of Yios (Son)
Σ - Sigma is the fist letter of Soter (Savior)
The Greek letters Alpha and Omega also both look like fish. The little alpha looks like a fish swimming right to left, and the Omega looks like a fish swimming up. Jesus is the Alpha and Omega (Rev 1:8).
The fish has Biblical significance. Jonah was swallowed by a fish (Jonah 1:17). Several of the disciples were fishermen (Peter, Andrew, James, John). Jesus told his disciples to be be "fishers of men" (Mark 1:17). Jesus did miracles involving fish - feeding the 5000 (Matt 14:18-21), and helping the disciples to catch fish (John 21:6). Jesus also proved he was physically risen by eating a fish (Luke 24:40-43).
Tradition has it that that early Christians used the fish symbol to identify each other during times of persecution. If a believer met a stranger and thought the stranger might also be a believer, he would draw the top half of the fish in the dirt.
If the stranger was a believer he would know to complete the other half of the symbol, and the two believers would be safe to acknowledge each other. If not, the non-believer would just think the other person was a little loopy for drawing in the dirt. Hopefully the early Christians were better at drawing than I am.
In early Christianity the fish and dove were common Christian symbols, more so than the cross. Clement of Alexandria was the first Christian to mention the fish in writing. The Catholic Encyclopedia notes that:
the earliest literary reference to the symbolic fish is made by Clement of Alexandria, born about 150, who recommends his readers (The Pedagogue III.11) to have their seals engraved with a dove or a fish. Clement did not consider it necessary to give any reason for this recommendation, from which it may be safely be inferred that the meaning of both symbols was unnecessary.Today the fish is quickly recognizable as part of the Christian subculture. According to Wikipedia, the modern fish movement was started by some Australian university students. Over the last forty years the symbol has become common again. Today it is cliche. You can get your fish auto emblem, fish T-shirt, or fish jewelry.
Darwinians have their fish too. Perhaps you have seen it on a car or two. The Darwinian fish swims from left to right, whereas the Christian fish always swims from right to left. The Darwinian fish has feet, emphasizing their belief that humans evolved from sea creatures.
And of course the Christian subculture never misses a beat. Not to be outdone, you can buy a Christian fish eating a Darwin fish.
The fish has evolved a long way over the years, and that is no fish story. :)