It is an idiom. It means you don't care (and it is emphatic). Idioms don't have to make sense.
This one does make sense though. You can read it as.. I care so little that I couldn't possible care any less.
, The "less" is a quantifier on how much you are caring (I hope that helps). It is saying you are caring the absolute minimum amount possible.
You also hear Americans say the opposite "I could care less", which means the same thing even though it seems to be saying the opposite.
But, as I told you, idioms don't have to make sense.