The part of a roof that extends beyond the side wall.
Merriam-Webster Online Dictionary
eave (noun)1.
the lower border of a roof that overhangs the wall - usually used in plural
2.
a projecting edge (as of a hill) - usually used in plural
eave (Wikipedia)
Italianate eaves with decorative support brackets
The eaves are the edges of the roof which overhang the face of a wall and, normally, project beyond the side of a building. The eaves form an overhang to throw water clear of the walls and may be highly decorated as part of an architectural style, such as the Chinese dougong bracket systems.