The Blue Moon is simply the name for a second full moon in a single month, which only happens about once a year. For some people this is a special occurrence in which to do powerful spellwork but it is really up to you if the Blue Moon has significance in your practice. I personally don't see it as very different than any other full moon but that's just me.
A blue moon is not the 2nd full moon in a month. This myth started in the 1980's when a lazy editor of an astronomy magazine didn't do her proper research. This full moon at the end of January is NOT a blue moon, dispite what you will read online.
Just think about this, a full moon happens the instant the Moon / Earth / Sun are in a stright line with the Earth in the middle. This is an exact moment and happens a tthe same time around the Earth. So the time on your watch depends on the timezone you are in. Therefore, if a full moon happens on January 31 in your timezone, that same full moon will happen on February 1 to someone in an earlier timezone. You will be both be looking at the exact same Moon, but for one of you it is the 2nd full Moon in January and the other it is the first full Moon in February. One would be a blue Moon, the other would not. How is that possible?
However, just like each month SHOULD have 1 full Moon, each Season SHOULD have 3 full Moons. But not always, sometimes a season will have 4 full Moons. When a season has 4 full Moons, the 3rd full Moon is a Blue Moon.
Most ancient cultures have specual names for certain Moons (Harvest Moon as an example, is the last full Moon of Summer). Even if we don't know all the names of the full Moons we can simply call them: 1st full Moon of Season, 2nd Full Moon of Season, and Last Full Moon of Season.
This is important because we can describe all biological activity on the planet with those descriptions of the Moon. We can predict with great accuracy when bird's eggs will hatch, insects will spawn, and wild plants will bloom exactly with these terms. All very important information if you are a farmer, or if your civilization just likes food.
Interestingly enough, when a season has 4 full Moons, we can refer to the Moons as 1st, 2nd, Blue, and Last, and we do not need to change the information about what happens during the 1st, 2nd, and Last full Moons.
This is why Blue Moons are important to every ancient civilization. Nature simply "ignores" Blue Moons. If you live in a city then this is nothing more than trivia, but agriculture still relies on the cycles of the moon to ensure crops grow and get fertilized at the best times and animal herds give birth at the optimal time to ensure the highest survual rates of the young.
February: No Full Moon, an rare event where February will not have a full moon last event was back in the 1999 and the other was in 1980 then next time February won't have a full moon will be in the year 2037
March 1st: The Full Worm Moon
March 31: The Full Sap Moon
April 29: The Full Pink Moon
May 29: The Full Flower Moon
June 28: The Full Strawberry Moon
July 28: The Full Buck Moon, during this time there will be a full total eclipse of the moon during this time