Her definition of "Emotional Labor" is most succinctly: Work performed with the intention of creating a feeling. Additionally, it's important in such roles that you manage your own feelings: You might need to be nicer or less nice in your role than you're typically comfortable with.
Her examples are social workers, teachers, flight attendants. It might also be a clown who is paid to make kids feel happy at a party even if the clown is really sad that day.
The inventor of the term wants to be clear that there is no gender specificity to it and that it might be a tool used by the feminist movement to classify work mostly done by women as emotional work because women are emotional, but that line of thinking shuts down conversations about emotional work that apply to all parties involved regardless of gender.