In the English-speaking world,at least as early as the 17ᵗʰ century –present, a unit of volume used to measure sawn lumber, = 144 cubic inches, but see below. Abbr, bd ft.

Currently, in calculating board feet for boards, it is customary to assume that boards less than 1 inch thick are 1 inch thick, even if after surfacing they are thinner than that. For boards thicker than 1 inch the actual thickness is used. However, the number of board feet in two-by-fours and similar pieces of wood (which are not “boards,” but dimension lumber) is calculated on the basis of their nominal size (as if they were really 2″ by 4″, for example).

Because for many years North America was the largest exporter of lumber, like many lumber terms the board foot has spread around the world (for example, the Ryukyu Islands (UN1966).

For a rule for estimating the number of board feet in a log, see Scribner-Doyle Rule.

sources

First, herein you must know, that a foot of Timber is a foot
square every way, viz. in length, breadth, and thicknesse : so that it is
twelve times more then a foot of Board; a foot of Board being but 144 Inches,
but a foot of Timber is 1728 Inches; and every Inch is square, like a Die, and
so is the foot also supposed to be; or if it want of this, either in breadth or
in thickness, it must have it in length.

Henry Phillippes. The Purchasers Pattern. 2nd ed., corrected and enlarged.
London: Printed for R. & W. Leybourn, for T. Pierrepont..., 1654.
Page 182.