A teetering system has zero offset. The aircraft hangs underneath a single point of suspension. A bit like a "T" with the vertical part being the mast, and the horizontal bit being the disc. There is a simple loose bolt attaching the mast to the disc. The disc can tilt without really moving the mast. it doesn't have a Moment.
When the disc is tilted by cyclic input, the disc then pulls on the top of the mast, and the fuselage follows a little later, like a bucket of water under a handle. Get the bucket moving, then suddenly stop the handle, and watch the bucket continue forward but then swinging up because its suspension point has stopped. The water doesn't spill, but there is delay between the movements of the handle, and the bucket following. This is zero offset. In the hover, you can waggle the cyclic like crazy, but the fuselage doesn't do much.
With a fully rigid system, the T no longer has a bolt or hinge. the blades are attached at the ends of the T, and are a bit flexible. Move the horizontal disc by tilting it, and immediately the mast is forced to follow. This can cause some big stresses. The disc now has a Moment over the mast, and depending on how far out from the mast are the blade attachments, the moment generated will be more or less. This is the amount of Offset.
In the air, it means that the aircraft is very responsive, and in fact for the BO105 and BK117, they are aerobatic, and can generate -1g safely. (A teetering head must maintain +1g to be safe.) The downside is that the fuselage follows the disc very rapidly, making the ride a bit upsetting for the passengers if the pilot is at all aggressive.
On the ground, just moving the cyclic can exceed the mast's safe limits, so there is usually a Mast Moment Indicator fitted to reduce the chances of breaking something. Slope landings get a bit tricky.