Plain-language summary of why Uranus and Neptune are different than Earth in having large offsets of their dipole field?
Earth's rotation is an important factor in contributing to the generation of the field, and helping to stabilise the form of it. The rotation influences the flow of compositionally convecting material deep within the outer core, forming cylindrical rolls that align along the rotation axis (a Coriolis effect).
While Earth's field polarity may reverse occasionally, it is to a good approximation (and we believe predominantly has always been) a roughly centred dipole, aligned roughly with the rotation axis of the Earth because of the influence of Earth's rotation.
For Uranus and Neptune, this is not the case. The centre of their dipoles are significantly offset from their centres of mass, the axes of the dipoles are significantly offset from the rotation axes.
For both Uranus and Neptune, magnetic field generation is believed to occur in flowing material much closer to the planets' surfaces (due to the very different composition of ice giants versus the terrestrial Earth). With flow constrained in a relatively thin layer near the surface, planet rotation does not have a strong influence on the form of the convective motion, so the field that results is not particularly tied to how the planet rotates.
This article gives a good idea of how the geometry of the convecting flow region can lead to Earth-like or Neptune/Uranus-like magnetic fields.