Distilled water for plants

I was wondering why my house plants are doing so bad since I give them Distilled water ? Don't get me wrong because for years I have been drinking distilled water by myself, but out of curiosity I am looking for an explanation why plants don't like distilled water. If rain water is also just distilled water then maybe there is really a difference between man made distilled water and rainwater ?! Just trying to figure out what exactly that might be. More then one opinion are more then welcome.