I've never really paid much attention to fishing when the moon is out or not and just fish whenever I feel like fishing or when I have time to fish.
But some people believe that fish become more active on specific Lunar Phases and not active on others or less active.
Also for some people the believe that fishing is very poor for a couple days around a full moon because the fish are feeding more at night.
Still I've never paid attention to it and I personally don't believe the moon has anything to do with fishing.
I wouldn't worry about it and just go fishing anytime you want too or able to fish.
In my opinion it's just a superstition about the Moon affecting fishing.