A board foot is the standard unit for measuring and pricing lumber in North America. It represents a volume of wood, not just a length. One board foot equals a piece of wood that is 1 inch thick, 12 inches wide, and 12 inches long.
The reason we use board feet instead of just linear feet is that lumber comes in many different widths and thicknesses. A 1x12 board and a 2x6 board might be the same length, but they contain very different amounts of wood. Board feet capture all three dimensions in one number.
You'll see board feet abbreviated as BF, FBM (foot board measure), or BDFT. When pricing lumber, especially hardwood, the price is almost always quoted per board foot.