The term davenport can refer to one of two things: a type of sofa or a type of writing desk.
Davenport, the Sofa: The term davenport for sofa began around 1900, when the Boston furniture manufacturer Irving & Casson & Davenport created a boxy sofa. With the popularity of this type of sofa, davenport became a generic term for any sofa. It is not very commonly used today, and the term is usually used by the generation that was born before World War II. Davenport can also refer to a sofa bed.
Davenport, the Desk:The second known use for the term davenport is for a small British desk. This desk was originally made in the late 18th century for a Captain Davenport who commissioned it. The davenport desk has a slanting top that can be lifted up. The desk has drawers and cupboards that open on the side, not the front. This useful, functional piece of furniture is still made and Captain davenport's name lives on, although we don't know anything else about him.