Well, resultant force must refer to something but I'm not sure what it is. Suppose we are talking about a change in the weather... There is no additional force due to the change in weather, and the plane continues to fly steadily.

"The aeroplane [American variant: airplane] is subject to no resultant force." = The airplane is not being affected by a combination of forces. "and continues in its state of unaccelerated flight." = The speed of the airplane is not increasing as it flies. "steady motion in a straight and level line" = it (the airplane) moves evenly and uniformly, and in a straight line which neither goes up nor down (which neither gains nor loses altitude)