If you're incautious, you don't worry about problems that might come up — you're a little irresponsible. An incautious person might paddle off in a kayak without putting a life jacket on.
Incautious behavior might include betting your whole paycheck on a poker game, bringing six stray dogs home, or lighting a bottle rocket and launching it from your hand. An incautious child is probably used to hearing adults calling, "Be careful!" Incautious combines the "not" prefix in- and cautious, or "careful," from its Latin root cautionem, "caution, care, or foresight."