It is that portion of metal ductwork that connects the boiler proper to the stack. Usually starting directly above or outboard the boiler exhaust damper if one is installed. Breaching in it's simplest form, adapts the size and shape of the boiler exhaust flange to that of the stack pipe.
Breeching, or sometimes spelled 'breaching', can be an extensive and rather elaborate configuration when several boilers need to be connected to a single stack.