What is the principal representation?

It could be one of many things. Probably it is the natural representation of whatever kind of object you care about acting on itself by left (or right) multiplication. Where did you come across the phrase if it isn't defined anywhere?

 

In what way is that not the definition of the principal (aka trivial) representation?

 

I have no idea. Perhaps when Isaacs wrote his book (a long time ago), that was what they called it. It also has links with the principal block too. Some times things have two names. Some times one name has two meanings. That's just the way it crumbles cookie wise.