Something that is succinct is short and clear. If you're going to be interviewed on television about your new book and only have a five minute slot, you'll need to come up with a succinct version of your story.
Succinct, meaning "short and to the point," is from the Latin succingere, "to tuck up." Often after you write a long essay, you realize you probably could have said the same thing in one or two succinct pages. If something is too succinct, we might call it terse. Another synonym is concise, which implies that unnecessary material has been removed. It's the opposite of wordy.
