(a) Balanced forces are those forces whose resultant is zero. Unbalanced forces are those whose resultant is not zero.
When we push a box and it moves, that means it has some unbalanced forces working on it, or the resultant forces working on the box is not zero, that's why the box moved in the direction of the resultant force.
But, if we push a box and someone pushes the same box back from the other side with an equal and opposite force, then in that condition the box will not move. Because, the resultant force on the box would be zero, or we can say the forces are balanced on the box. So, there is no movement of the box.
(b) When we press a rubber ball between our hand, then forces acting on it are balanced, because the ball does not move when we press it. By pressing the ball between our hands, the ball gets deformed.