Nomadic dwarves who have chosen to settle down outside their kingdom. They may be estranged, banished or simply decided they liked where they ended up.
Communities of offshoot dwarves are regarded as followers of Marthammor Duin (http://forgottenrealms.wikia.com/wiki/Marthammor_Duin).
Duinians are no less honour bound, kind, racist, or dwarven then other dwarves; they've simply chosen to remain somewhere instead of return to their home kingdom. Perhaps one day they will (provided they're welcome back).