Intercultural communicative competence, or ICC, refers to the ability to understand cultures, including your own, and use this understanding to communicate with people from other cultures successfully.

Example
ICC could include understanding how gestures and the distance between speakers vary from culture to culture.

In the classroom
Ways to develop this competence include learners producing a written or online guide to their own country and culture for visitors, reading and discussing guides written by visitors, researching aspects of a target culture in various media including cinema, literature and television, giving presentations on aspects of the target culture, and exploiting the teacher's own expertise of their own culture.

Further links:

https://www.teachingenglish.org.uk/article/making-culture-happen-english-language-classroom

https://www.teachingenglish.org.uk/article/storytelling-celebrate-cultural-diversity

https://www.teachingenglish.org.uk/article/culture-fifth-language-skill

https://www.teachingenglish.org.uk/article/other-cultures