Taut means "tight, not slack." "The tightrope ought to be taut and not dangling down by the lion cage."
It sounds like the word "taught" and means stretched tight, like a rope, muscles, or even nerves. It's nice to have a taut body with tight muscles, but not so great to have a taut mind — tightly wound and tense. "The Olympic gymnast's taut body was something she worked hard for, but she gave a taut reply to reporters who asked her so many questions about her past, which she wished to keep a secret." Taut is derived from an Old English word, meaning basically "to pull." If you're fishing, you're happy when your line becomes taut, because there's probably a fish pulling at it. Or an old boot.