Soffit

Eaves of a house in Northern Australia. The white underside would be referred to as a soffit. In this example the soffit is fixed to the slope of the rafters. The dark grey fascia boards form the outer edge and have a groove to receive the soffit lining sheets which cover the rafter tails.
Boxed in soffit on a house in Northern Florida, United States. In this example the soffit material is 12 inches wide and made from center lanced U groove perforated sections of vinyl in a return fashion and fixed to the bottom chord of a truss roofing system extending beyond the exterior wall.
Interior soffit box providing attachment points for kitchen ventilation hoods.
Four images of a soffit being built to hide a retrofitted ventilation duct.

A soffit is an exterior or interior architectural feature, generally the horizontal, aloft underside of any construction element. Its archetypal form, sometimes incorporating or implying the projection of beams, rafters or trusses over the exterior of supporting walls, is the underside of eaves (to connect a supporting wall to projecting edge(s) of the roof). The vertical band at the edge of the roof is called a fascia. A soffit of an arch is frequently called an intrados.