Can someone explain the earth's figure axis and the effect the quake in Chile will have on the earth to me?

It is like a spinning dancer moving her arms towards her body; due to the temblor the planet has now its m closer to its (figure) axis, therefore a slight increase in spinning takes place so the (rotational) momentum is maintained. You can test the effect by sitting on a rotating office chair, taking a rotational impulse with your arms spread and then moving them towards your chest - you should increase your rotation speed ! Cheers, from Chile