Conformed dimentions are dimensions which are common to the cubes.(cubes are the schemas contains facts and dimension tables)

Consider Cube-1 contains F1,D1,D2,D3 and Cube-2 contains F2,D1,D2,D4 are the Facts and Dimensions

here D1,D2 are the Conformed Dimensions one dimension can share with more fact tables through primary key and foreign key relationship.