Where everyone is at liberty to do whatever they want, factors like wealth and good looks and charm make some people "more equal than others". Those without wealth and good looks and charm can only gain equality by force of numbers, which has the effect of taking away some of the liberty of the rich and powerful to do whatever they want.

There's a direct relationship between the two, but it's more like the moon's relationship with the Earth - equality has som effect on liberty, like the tides, but liberty is like the earth's gravity, keeping the moon in orbit.