A cavity wall is made up of two leaves of masonry (bricks/stone/blockwork) with a cavity ‘gap’ between them to stop moisture transferring from the outer leaf to the inner leaf. If the gap is filled (e.g. with rubble from the construction process or with poorly installed insulation) moisture can transfer across the cavity to the inside of the wall.
Source of moisture: rainwater as penetrating damp bridging the cavity.
Repair: clear the cavity of construction rubble (and damp insulation if any), then reinstall suitable insulation if previously existed (not necessarily inside the cavity wall void).