It's always been a bit of costuming advice bordering on a rule, so I've gone ahead and made it an official part of the dress code. Wearing shoes that are unsuitable for heavy activity, such as high heels or sandals, is now against the rules.
I can't give you a strict definition beyond advising common sense. The objective is to wear something that won't cause you to fall and break your face while running or fighting. "High heels" are just one example, but stability is the only real litmus test.
If it's safe, wear it. Nobody will take exception unless it's likely to cause injury.
Could you possibly define "high heel"? I know a few pairs of shoes, such as riding boots and what not, that have a heel between 1-2 inches that are quite stable, sturdy and easy to move in. Would that count as breaking the dress code? I would really like to know so that myself or someone else doesn't end up with a pair of shoes that are un-useable at orn because of a different definition of a heel.