Your site will make excellent lunch-hour reading -- thanks!
Libration manifests itself in two ways. Side-to-side libration is caused by the elliptical orbit. As we're well aware, the Moon is tidally locked and has a rotation rate equivalent to its orbital period. Its rotation rate is stable and, for observational purposes, constant. But Kepler's second law tells us that in an elliptical orbit the Moon will speed up and slow down as it moves through its orbit. It moves faster approaching perigee and slower approaching apogee. This means that during each revolution, the Moon "gets ahead of itself" and "behind itself" at different times, turning to show us glimpses of the sides. During its approach toward apogee, for example, the Moon speeds ahead and its constant rotation rate doesn't turn it to face us perfectly; we see a bit of its trailing edge through apogee. Conversely through perigee we see its leading edge. From Earth's perspective, the Moon appears to twist left and right during its cycle.
Vertical libration is caused by the difference between the Moon's rotational axis and its orbital inclination. They aren't the same value. Like most celestial bodies, the Moon's rotational axis is not perfectly perpendicular to the plane in which it orbits. But the axis is fixed in space reasonably stably for observational purposes. This means during one part of its orbit, its north pole points more toward us than at the opposite side, where it points away from us. This lets us see the north polar regions at some times and the south polar regions at other times.
When you combine the two motions the Moon indeed appears to wobble over the course of a lunar month like a spinning top about to fall over. (Unless you're in Inception dream space.)
If you lived on a lunar surface base, the Earth would stay in roughly the same place in the sky but would describe a figure-eight motion around a fixed point due to lunar libration. The Earth would also exhibit monthly phases, but in the mirror-image direction that we see of the Moon from Earth.
Who wants to hear about nutation?
