A blue moon happens when there are two full moons in one month. The second full moon is known as a "blue moon". They only happen once every few years which is where the term "once in a blue moon" comes from. In years they do happen, they can occur twice in the same year. This type of blue moon is not actually blue in colour.
There is also a rare occurence where the moon appears a bit blue in color -- this usually happens when there are smoke particles in the air (for example, due to forest fires). It isn't something that's predictable.