Which part do you not understand? An implicit surface is defined by F(x,y,z) = 0. Implicit surfaces can be rendered by checking whether the camera ray going th

Which part do you not understand? An implicit surface is defined by F(x,y,z) = 0. Implicit surfaces can be rendered by checking whether the camera ray going through pixel x,y intersects the surface or not. An axis-aligned bounding box (AABB) in 3D is the product of intervals [x_min, x_max]x[y_min, y_max]x[z_min, z_max]. The interval extension of F(x,y,z) gives you an interval [F_min, F_max] for such an AABB. If [F_min, F_max] doesn't contain 0, then you can discard the whole AABB for rendering purposes, because the surface is guaranteed to be not there. This can speed up rendering substantially.