[gsodonis]

As the name suggests, hub centric wheels use a lip machined on the end of a hub to center the wheel on the hub.
Bolt centric wheels rely on the lug nuts to center the wheel on the hub (each tapered lug nut centers each corresponding mating wheel bolt hole to the hub assembly).

From an engineering perspective, the wheel studs (or bolts depending on manufacturer) do double duty in bolt centric applications. The studs must withstand the shear forces produced by the rotation of the wheel and they must also withstand the shear forces produced by vertical forces generated by the suspension as it absorbs road irregularities.

In hub centric applications, the shear forces from wheel rotation are the same, but the forces generated by the suspension are transfered to the hub through the wheel/hub lip interface and not throuigh the wheel studs/bolts.

Most of this is invisible to the driver under normal circumstances, but in off road and racing applications, hub centric is more durable and preferred.

What happens if you install road wheels without hub centering rings?
From a safety perspective, most likely nothing as the wheel/braking systems of most cars are engineered with pretty big factors of safety (they're essentially over engineered).

In my experience, I once had a set of +1 size aftermarket wheels that I installed on my wife's minivan. The steering wheel shook horribly and the tire dealer tried three times to re-balance the wheels without success. When I asked about hub centering rings, I was told that the wheel manufacturer claimed that my Honda Odyssey didn't need them as it was bolt centric. I chose not to believe them and bought a set anyway. As soon as I installed the centering rings, all of the steering wheel vibration disappeared.

Moral of the story, if you try and fit aftermarket or non-OEM wheels onto your vehicle and you get a steering wheel vibrations that wheel balancing won't eliminate, try a set of hub centering rings and it might just do the trick.