This dates back from early Christianity. Original jewish fast days were Tuesday and Thursday - Christians moved them to Wednesday and Friday - Jesus was betrayed on Wednesday, and crucified on Friday. The notion of fasting meant leaving something out of the diet as a dicipline of the soul. Meat was seen as a luxery because you had to own cattle, or be able to afford to buy it. Fish could be caught by anyone, so equated with a poor person's diet. So the tradition evolved of abstaining from meat on the fast days, and eating fish as a substitute.
I was brought up Church of England and we were only allowed to eat fish on Good Friday, but my dad is Catholic and he was brought up to only eat fish on all Fridays. But every Friday the fishmongers' van parks in our village and there's always a queue...
Until Vatican II (1962), meatless Friday was a standard Catholic practice. It was supposed to be a form of sacrifice, you see. After Vatican II, it became permissible for Catholics to eat meat on Fridays, but many staunch Catholics, or older ones, still stick to fish or macaroni and cheese.