The immediate application of it is that when you choose a DB, you should be able to tell if it's either CP or AP. The field is full of subtleties (eg Network is not 100% reliable so no system should be CA - it's way subtler but that is the gist of it. I'm no expert btw).
Lots of DB vendors have tried to circumvent the therorem by introducing their own concepts or stretching the definitions. "We can beat the CAP theorem"