Recall that in 3D, we need three directions to form a basis for the space. Hence given some curve and tangent and normal vectors and , we can find a third vector that is orthogonal to both the unit tangent vector and unit normal vector. The cross product of two vectors in 3D space is orthogonal to both vectors, so we can define the binormal vector by:
These three vectors together give us a local basis that we can use to compute useful things about the curve (forces, etc).