Hello,
There are many reasons why flowers close and open, but one of the biggest has to do with insects. Remember, many insects feed off the nectar of flowers. When they go to eat from a flower, they get pollen on them. Pollen is the powerdy stuff that makes you sneeze. Anyway, when they fly to another flower, they take the pollen with them. If the plant is lucky, it gets some of the pollen from another flower, and can make seeds.
Now insects, like people, have different schedules. Some of them fly in the morning, some of them fly in the afternoon. Some of them don't fly at all; they crawl. Anyway, the flower has to be open for the insects, otherwise the insects don't get to eat and the flowers got get their pollen. That's one of the reasons that flowers open and close at different times.

This may have to do with several reasons, depending on the type of flowering plant.

1) The plant may have evolved to be pollinated most successfully (over a long period of time) by an insect which only comes out at night.

2) The plant may attract unwanted attention from other insects or animals if it stays open either during the day or night, forcing it to adapt and be open at only one time or another.

Well, step one in answering that question would be to ask "what do flowers do?" Flowers let one plant exchange DNA (genes) with another plant. It is part of their reproduction. So how does the pollen (containing DNA) get from one plant to another? One way is by taking advantage of pollinators, which are animals that visit the flower to get something good (like what?). They get covered with pollen, then visit the next flower, where some of the pollen rubs off. What kind of animals do this? Some flowers are pollinated by flying mammals (what do we call them?). Why would the flowers they pollinate have to be open at night?

For answers and photos, go to this page:
http://imagers.gsfc.nasa.gov/adventure/saguaro.html

Thanks for asking.