Emotional fidelity is the idea that love and/or emotional intimacy must be kept exclusive between partners. It is usually a tenet of monogamy (where two people remain both physically and emotionally exclusive) and of swingers (where two people remain emotionally exclusive, but not physically).
In other words, emotional fidelity means being in love with one person, and falling in love with another (even in the absence of physical intimacy) can constitute cheating.
More About Emotional Fidelity
Emotional fidelity is inherent to monogamous relationships. However, polyamory challenges the concept that love must be reserved to a monogamous, and opens up the possibility of being in love with more than one person.
It can be difficult for newly open or polyamorous couples to let go of emotional fidelity. The fear of abandonment, of being removed from a partner's affection, can be very strong. Another term that describes this fear is the "scarcity mindset": the belief that love is finite and that if it is given to another person, then you will have less of it as a consequence. In other words: if your partner loves someone else, they love you less (or not at all).
Deeply ingrained in the monogamous couple model, the scarcity mindset is often the biggest obstacle to happy and fulfilling polyamorous relationships.