Spring tides occur twice per 28 day lunar cycle (month), firstly during the full moon and secondly during the new moon. It is generally accepted that fishing is best over spring tides, from three days before spring tide and lasting until three days after, with fish being more active during these periods, all other factors being equal. This could be because there is then more surf and swell activity which dislodges more bait organisms from the sand, reefs and rocks, but that is just a guess.
Don't believe for one second that you can't catch fish at other times, though, or that fishing over spring tides will guarantee you a catch. It could be useful to plan your fishing trips over these periods though, eg. make sure that you take your leave over a spring tide, rather than over a neap tide. With the extra low tides during spring tide it is also easier to collect bait from the rocks, or you could create a good chum hole during low spring tide that will bring in the fish once the tide turns to incoming.
A full moon has the added benefit over the new moon that you can fish at night without too much effort with the moon providing enough light unless it's overcast.
I hope this helps.
PS: Neap tides occur during the moon's "first quarter" and "last quarter", which you could describe as "half moon", neither full nor dark.