The cell theory mainly clarifies the diversity of cells or the unity of the biological world.

①The cell theory demonstrates the unity of the biological world, but does not reveal the diversity of animal and plant cells. ①Wrong.

② One of the main contents of the cell theory is that "animals and plants are composed of cells", which shows the unity of the structure of living organisms, ② correct.

③The cell theory does not explain the difference between animal cells and plant cells, nor does it explain the differences in the biological world. ③Wrong.

④The cell theory explains the unity of cells, ④Correct.

So the answer is: D.