The moon is slowly receding from the Earth, by a few metres per year. As it recedes, it orbital angular momentum increases. Total angular momentum is conserved, so the angular momentum of the Earth must decrease - the Earth slows down.
On top of this, as the moon orbits the earth, it pulls the Earths oceans and liquid interior, creating tides of high water and low water, and friction internal to the Earth. The moon orbits the Earth once every twenty eight days, but the Earth rotates on its axis once every twenty four hours. Because the orbit of the moon is slower than the rotation of the Earth, the rotation of the Earth is slowed by friction between the Earth and the movement of the oceans as they follow the orbit of the moon.
Because of these factors, the length of a day is gradually increasing, and every so often we must insert a 'leap second' into into a year to correct for this.
When the moon was formed billions of years ago, the length of a day on Earth was only two or three hours. The effect on the length of a moon day is much more significant, since the moon is smaller. Thelength of a moon day is 28 days - the same as the time it takes to orbit the Earth. Because of this we always see the same side of the moon.