The term probably means that have bothered to learn at least the basics about the people you share your homeland and the wider world with. For instance, that not all brown-skinned asians come from Pakistan,that many Africans have University degrtees and have never lived in a jungle,and even that 'our' number system is arabic, and phonetics semitic.
   When we lived in Leicester the new school cook at my wife's school was asked by the Headmaster to make sure that there was a daily vegetarian choice available for the many Hindu pupils who practised vegetarianism.
The first day.... What's for lunch, cook?
Beef Stew.
Good....what about the vegetarian alternative.
Beef Curry.

She could have been described as having little multicultural competence.