To be carefree is to be free of care! You have no troubles or worries. Being carefree is feeling happy and breezy, like the carefree days of summer before school starts.
To be carefree (one word) is to be happy and relaxed. People tend to be carefree when they're not working or thinking about work or school. Being carefree is the opposite of being stressed out. Carefree is not the same thing as careless — when you’re carefree, you haven't a care in the world and you might dance in a field of daisies. If you’re careless, you’re probably stomping on someone’s garden.