Cute little buzz words that don't really have any Java significance. They are just descriptors trying to convey how detailed the thing is. Coarse Grained security would be like: NO your applet can't write to my hard drive. Fine Grained might be: well you can write to my temp directory and you can read and write to my cookies, but not to anything else. I've seen it used to describe listeners - how detailed they listen. I've seen it used to describe the micro handling of text by JavaServerPages. I've seen it used to describe the order of parsing a java file, and the order of presenting execution rules. This is a fine grained explaination of your question (compared to my just saying "fine grained = more detailed).
"JavaRanch, where the deer and the Certified play" - David O'Meara