See the second paragraph under 'Tidal Evolution' here
https://en.wikipedia.org/wiki/Orbit_of_the_Moon#Tidal_evolution
but don't worry too much if you struggle to understand it. I used to teach Applied Maths to A-level but I had to read through it several times before it started making some sort of sense to me!
I didn't know it was moving away, but in general terms things are close to equilibrium, with the sun and other objects in solar system and perhaps in the galaxy pulling on each other.
Yes db's answer is comprehensive and easy to understand. Just to add that the reason the earth is slowing down is because of the distortive effect (the "tidal" effect that the Moon has upon it. The Moons gravitational effect stretches the Earth into an oval shape (the "high tides" in the seas being the manifestation of that). Such distortion slows a spherical object down. An easy way to see if an egg is raw or hard boiled (apart from cracking it!) is to spin it on its side. The raw egg will slow rapidly because the liquid gets thrown to the ends of the shell. The hard-boiled one spins for longer.
Tidal forces pull the Earth into an oval shape which is pulled forward with rotation so that the mean gravitational force of the Earth upon the Moon pulls it forward thereby accelerating the Moon's orbit causing an increase in the Moon's orbital distance.
I wonder that if, as the Moon's orbit moves away and therefore lengthens in duration, it has a noticeable effect on our climate. We could call "them" the green cheese movement.