This is how the universe is expanding. We know that we can draw a line in a square . Here line is 1dimension and the square is 2dimension. Similarly a square could be drawn on a cube . here square is 2 dimension and the cube is 3dimension. Similarly a point which is 0 dimension could be drawn on a line . Do not confuse between point and a dot . They are two different things. Also, a point could not be drawn on a square . A dot can be drawn . So we conclude that an object can have another object which is one dimension lower.So, if the space is 4d then the universe is 3d.[it is just an example]. So the universe is expanding into the space which is 1 dimension higher to it.