By having an intimate relationship with someone. When you are regularly telling them things about your day that bothered or pleased you and how they made you feel because you appreciate their input, while your SO just gets some version of "my day was fine," that is emotional cheating. In general, it is about making someone else your primary source of emotional fulfillment.

Marriage isn't intended to be purely about the sexual relationship, it is also a social and emotional partnership. Outsourcing that emotional partnership to someone outside the marriage without discussing it with your SO is no different from sleeping with someone else.