just like any other affair, but with no boning. where you have mutual feelings for someone NOT your significant other but you never hook up.
John: we had a total emotional affair.
John: I was emotionally cheating on Heather with you.
A pop psychology term which instills a sense of impropriety when describing Platonic and courtly love (and other forms of intimate non-sexual association). Since the relationships it defines are by definition chaste, its use is misleading and is often used manipulatively.
You call it coffee with a college professor, I call it an emotional affair.