Circuitous means indirect or roundabout. If you're in a hurry to get to the hospital where your wife is having a baby, you want to take the straightest, fastest way, not a circuitous one!
Circuitous comes from the Latin word circuitus meaning basically "a going around." If you're being circuitous it's like you're going around and around in circles. It can also refer to someone's manner or speech, if they are not being direct. For example, if you want someone to get you another piece of cake but just you sit there looking longingly at your empty plate, saying "More cake sure would be nice," then you're being circuitous. And annoying.