A board foot (bf) is a volume measurement of wood.  The number of board feet in a timber or board can be calculated by using the following formula:

# of board feet  =  ( Thickness in inches  x  Width in inches  x  Length in feet )  /  12

Examples:

(1) A 2" x 10" x 18' board contains 30 board feet:  (2 x 10 x 18) / 12 = 30 bf

(2) An 8" x 12" x 20' timber contains 160 board feet:  (8 x 12 x 20) / 12 = 160 bf

Note that lumber and timber thicknesses and widths can be (and, in fact, generally are) nominal (as opposed to "full" or "net").  The actual dimensions of a 2" x 10" x 18' board, for example, might be 1 1/2" x 9 1/4" x 18'.  The nominal dimensions are used in the board foot calcuation, not the actual dimensions.

If you are interested in an easier way to calculate board footages (and square footages and linear footages, for that matter,) check out Trestlewood's Board Footage Calculator.