Begin by imagining that the moon isn't quite a perfect sphere. One side is just a little bigger than the other. As the moon rotates, the heavier face will swing around towards the earth a little faster, and it will swing away from the earth a little slower, since it feels a stronger gravitational attraction via its larger mass.
Since gravity is a conservative force, you might think that this continues forever - but it doesn't! The moon isn't totally rigid; rocks can slide around both on the surface and even inside the moon. The heavier lump actually slides through the moon to try to stay facing the earth, which causes friction inside the moon. That friction heats up the rocks, but the heat is slowly lost into space.
Now we have a conservation of energy problem: the rotational energy of the moon is being converted to thermal energy in the rocks, and that thermal energy is being slowly leaked out of the system. The only resolution is that the rotation slowly stops over many millions of years.
Finally, let's return to our assumption of a small mass imbalance. Is this true? Almost certainly - all we need is the fact that the moon isn't a truly perfect sphere.