When you're careless about something, you're not giving it much attention or consideration. If you're careless about mowing the lawn, you might mow over your mother's prized daffodils without even noticing.
When you say, "I couldn't care less" about something, you're probably going to be pretty careless about it, too. If you couldn’t care less about your homework, then you'll approach it in a careless manner, without much thought or concentration. Careless is negative, but it’s a little less so when it means effortless and unstudied, the way you might bat away a bug with a careless swat. Interestingly, the root meaning of care is "grief," so careless is "without grief."