The part of a roof that sticks out past the side of a building is called the eaves. If you hear chirping outside your window, it may be birds nesting in the eaves of your house.
Eaves are an architectural feature that look good aesthetically, but they also serve the important purpose of directing rainwater away from the house. The word stems from the Old English efes, meaning "edge of a roof" and also "edge of a forest." You'll almost always see this word in its plural form. In fact, some dictionaries list eaves as both the singular and plural.