Tidal action is evidence of the moon's influence upon the waters of Earth. The "Best Days" to go fishing on the moon phase calendars show the days on which fish will tend to feed more aggressively. Using moon phases to plan fishing trips is only one factor in planning a fishing strategy.
You must also know the habits of the species! Trout and albacore fishing is usually slower around the full moon because the fish feed at night. Tides are strongest on the full moon which usually makes for the best sturgeon and striper fishing. Migratory fish often come into a river system in greater than average numbers on a higher tide, when weather conditions are favorable.