What happens to a flower after it is pollinated?

After a plant is pollinated, the pollen grains land on a receptive stigma and germinates, much like how a sperm cell fertilizes an egg cell. This then gives the plant enough chromosomes to produce a seed that can properly grow into a plant as its parents have.

Let me modify the above answer a little. The pollen grain carries a little packet of chromosomes, one half of the number in any cell of the parent plant. When the pollen grain lands on the stigma, it does indeed germinate and a long tube grows down the pistil to the ovary--that is what will become the fruit. Many, many pollen grains do this, in fact, at least one pollen grain for each seed. In the ovary are ovules that eventually become seeds. As the pollen tube grows down the pistil, one tube goes to each ovule and one little packet of chromosomes is deposited in each ovule.

The ovule has its own little pack of chromosomes, again one half of the number in any cell in the parent plant. These two halves get together and form one new cell that is now a combination of both parents. This cell divides and becomes the embryo in the seed. (If you open a peanut, between the two halves you see a little peanut plant--that is the embryo.)

Once the seed begins to grow and develop, phytohormones (plant hormones) are produced which cause the ovary to grow into a fruit which contains the seeds.