A sump is just another small tank underneath the main display tank where you can put equipment and things like that.
A refugium is just a section of your sump or another small tank plumbed in that usually holds some or all of: sand, rock rubble, and macro algae. It helps pull nutrients out of the water and also provides a good place to breed pods (little bugs that the fish eat).
LFS - local fish store
LPS - (coral) large polyp stony
SPS - (coral) small polyp stony
If you search the articles or FAQ on the bar at the top of the site i think there is an acronym list in there somewhere. Also the articles section has some great reading for beginners that will help to answer a lot of basic questions and give you some good background.