An eave is the part of the roof that extends out past the side walls. The edge of the roof is a complex bit of carpentry which includes the soffit (the underside of the eave) and the fascia (the vertical edge of the eave). The fascia and soffits can decay when gutters are not kept free of leaves and debris.
Efflorescence is a white, powdery substance of soluble salts that appear on the face of bricks or concrete as moisture travels through masonry; the salts remain as a residue on the surface once the moisture evaporates. This residue is harmless and can be removed with a stiff brush and water.
Efflorescence can be, however, an indication of rising damp, a destructive process where moisture from the ground is drawn up (or wicked) into a masonry wall if the wall is not protected with an intervening layer of impervious material, such as slate, tile, building felt, or metal. An experienced masonry contractor should be consulted to determine the best way to correct rising damp.