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. Incautious children are probably used to hearing adults telling them to be careful. Incautious is a combination of in-, "not" and cautious, "careful." It's derived from the Latin adjective incautus stemming from the noun cautionem, "caution, care, or foresight."