See here or see below for a nice visual depiction. Consequences of the wobbling (more technically known as precession) are: the north star, polaris, won’t always be the north star; the signs of the zodiac are always shifting (based on Greek times, when these things were first formulated, it’s off by one whole sign, so we’re actually a sign off from what newspaper horoscopes tell us we are) so they’re bound to not be true.

Graphic by Michael Paukner