Let's talk about sex!
Ok, we have established that corals are animals..right!? Now, let's discuss how corals reproduce!
To keep things simple, coral reproduction can be broken down into two categories; asexual and sexual reproduction.
Asexual reproduction occurs by fragmentation or budding/fission; both of which do NOT produce new genetic material.
Fragmentation was used here to produce Staghorn coral fragments - Fragmenting corals is a commonly used technique to rebuild coral reefs by cutting from healthy mother colonies and outplanting the fragments somewhere else! Fragmentation also occurs naturally via wave action, storms and by other animals on the reef.
Coral budding or fission - Budding or fission occurs when a parent polyp "buds" or "splits" respectively, forming a new colony that is an exact genetic replica of the parent polyp.
And finally sexual reproduction!
Sexual reproduction - The obvious goal of sexual reproduction is to produce planula larvae (coral babies). In simple terms, corals achieve this by (1) producing fertilized gametes within the body of a polyp i.e. brooding or (2) fertilize gametes outside of the poly in the water column i.e. broadcast spawning. The newly formed planula larva are attracted to light and naturally swim near the surface of the ocean for a number of days or weeks. The planula larvae will then fall back to the ocean floor, attach to a hard surface and begin multiplying (that is if they don't get eaten by a hungry predator!).
Of course, this is only a very simplified version of coral reproduction. If you have questions, please ask!