Coral: Living organisms. I like to compare them to plants that you would keep in your home, except a lot of them have literal "mouths" and need to be fed, since they don't move. They are beautiful additions to your tank, though take caution in adding them. Some need an older, established tank, meaning it's been around for awhile and has a lot of the bacteria that gets rid of waste, better explained below. Some need strong lighting, such as T5s or Metal Haillades (sp on that, lol), and certian salinity and specific gravity, which is the ammount of salt in your tank. There are a lot of other things about keeping them, do your research before you get anything.
Live Rock (and Live Sand, same concept): Live rock isn't literally "alive". It has been in the water before, and has grown important algeas and micro-organisms on it, such as important bacteria that helps break down uneaten fish food, waste, and other unwated products in your tank. They often come with "hitch hikers", which are larger organisms, such as some corals, shrimp, snails, and some other things that could be harmful, though many arn't and it's cool to see what surprises you get. =)
Sump: A sump is usually another tank set up below. It is meant to hide your equipment to give your display tank a more "natural" feel, and increase water ammount. I have a thirty gallon display tank, and a twenty gallon sump. Technically my tank has fifty gallons now. Also, there are many filter elements that can be added to your sump, such as a refugium an protein skimmer, that make your water quality better for your livestock. I built my own using a DIY (do it yourself) on youtuve. I can give you the link if you'd like.
As I said, do your research. The most important thing in the hobby is
paitence. There needs to be time in between adding livestock so your tank can adjust to having more waste and things living in it. The bacteria need to produce more, ect. Also, since your new at this, make sure you read about your tanks cycle. EXTREEMLY IMPORTANT! I'm pretty new at this too, but know a little bit. It's all about expearence. We can learn together.
Welcome to SWF =)