We all know that sunflower's flowers move so that they face the sun. But the photosynthesis happens in leaves, not in flowers. Why is then so important for a sunflower to move its flower, if its leaves more or less stay put?
Sunflowers are tall, so contrary to most of the compositae (Asteraceae), the flowers appear vertically (and not horizontally). In this manner bees will see the flowers without the need to fly very high.
But this means the flower is seen just in one direction. By moving towards the sun, the sunflower will be never in shadow, and it will be very visible to bees. Bees' eyes seem not to be so good.
Note: when it makes seeds, the flower will turn down, so that it will allow just some small birds to eat the seeds (large birds will possibly break the flower, and eat too much, so not spreading the seeds around).
So sunflowers are just voluble flowers: they want to be seen. Note: the petals are just for display, the real fertile flowers are in the inside circle. In general flowers are a very expensive gift to insects (petals, nectar, pollen) just to try to have pollination between the same species.