What term describes a horizontal board spanning the top of columns or walls?

The correct term for a horizontal board that spans the top of columns or walls is "fascia." Fascia boards are typically installed at the edge of the roofline, serving both functional and aesthetic purposes. They help to support the bottom edge of the roof and provide a finished look to the eaves. Fascia can also serve as a mounting point for gutters, which further emphasizes its importance in residential construction.

In contrast, rafters are sloped beams that support the roof structure and are not typically horizontal. Trim refers to decorative elements that finish off carpentry details; it does not specifically describe a structural component like the fascia. A ledger is a horizontal board used to support joists or beams, generally associated with decks or floors, but again, it does not serve the same function as fascia in the context of spanning the top of walls or columns. Hence, fascia is the most accurate term for the described component.