Great question. I usually use em-dashes for appositives in long sentences that already have commas in them. So they are “fall-back commas” kind of like brackets are fall-back parenthesis.
I also use them to tack a fragment onto a sentence without having to worry about having an noun and an object.
Here’s a proper explanation of how these work: http://grammarist.com/grammar/emdash/
If you’d be interested in boiling these three uses down into as short and memorable an explanation as possible, we could include it in the style guide 😊