As most of you are likely to know, a blue moon does not refer to the colour of the moon, but is commonly understood to mean those rare occasions when there occur two full moons within one calendar month.
The moon takes 27,32 days to orbit Earth. This is known as a sidereal month. However, the period from one full moon to the next is not equal to one lunar orbit. It is the period it takes from the moon being in opposition to the sun to being so again. This is a bit longer than a sidereal month, because Earth moves on along its orbit around the sun so that the moon has a little bit more than an orbit (360 degrees) to travel from one full moon to the next. This is known as a synodic month and is on average 29,53 days, as Rigil Kent has pointed out. For an animated graphic to illustrate the difference between a sidereal month and a synodic month, look here.
Whereas a sidereal month is rather constant, the length of a synodic month varies somewhat. This is because Earth’s orbit around the sun is not circular, but slightly elliptical with the sun at one of the focal points of the ellipse. When Earth approaches the point where it is closest to the sun, it accelerates a bit because it is “falling” closer to the sun. The point where it is closest to the sun is known as perihelion and occurs early in January. From this point on Earth slows down slightly in its orbit until it reaches its furthest point from the sun, aphelion, early in July. Because Earth subscribes a bigger angle in its orbit at perihelion during one sidereal month, the moon has to travel a little bit further to catch up to opposition than at aphelion. In consequence the length of a synodic month varies between 29,18 days near aphelion and 29,93 days near perihelion. It always exceeds 29 days though and a blue moon in February is therefore not possible. Because February is close to perihelion, the length of the synodic month exceeds the average 29,53 days at that time of the year.
February months with no full moon do occasionally occur.
P.S. There is another definition of a blue moon as being the third of four full moons occurring within one astronomical season.More reading.