Some mental states are selected for (by Darwinian natural or sexual selection) because they cause specific kinds of behavior. I think an emotion is such a mental state combined with a perception on the part of the agent that they are in that state.
The perception aspect of it is essential, I think. We may talk in shorthand of “angry wasps”, but wasps only behave as if they’re angry, unlike dogs, say. To genuinely have an emotion of anger, agents must perceive themselves as being in that state, so that they have a distinctive experience of it, and can reflect on it a bit, maybe even giving some thought to “giving it free rein” or “reining it in”.
To perceive our own mental states, we need to recognize them for what they are. This involves identifying them as belonging to this or that category. How do we learn to do this? First, we learn to recognize the mental state in question by the distinctive behavior it causes in others. Then we learn to “spot the signs” or inner feelings in ourselves — urges, if you like — that accompany our own propensity to behave in similar distinct ways.
So how “private” are emotions? Natural selection creates and shapes emotions for the behavior they cause: in other words they have a public purpose. And furthermore, we initially identify and categorize emotions with reference to public criteria. This makes emotions a much more public matter than has traditionally been supposed. Like the identification and categorization of private experiences of color, the identification, categorization, and therefore understanding of emotions depends on shared activities. Yes, with effort we can sometimes keep an emotion under wraps, but this is the exception rather than the rule. And we usually only try to do so when we think it’s to our social advantage to do so, social advantage being another thing we learn to recognize through swimming in a social sea.
Obviously, emotions have both public and private aspects, and because it can be advantageous to have a particular emotion or to seem to others to have it, they are liable to be faked. (Keeping emotions under wraps as mentioned above is one sort of fakery.) In other words, in some respects they work like signals. Rather as butterfly wings can exhibit fake eyes, some expressions of emotion aren’t quite what they seem. There can be social advantages in faking contrition, for example, or in faking emotional attachment.
Here things get a bit murky, so what I say here is tentative. In general, the possibility of fakery can result in a sort of arms race in which potential dupes get better and better at spotting fakery, while fakers get better and better at producing it. Usually, “costs” increase — ideally to the point where fakers are no longer prepared to pay. But close to that threshhold, both fakers and non-fakers pay a lot. Furthermore, there is a blurred line between fake and genuine emotions, because emotions are not literally true or false. Both fake and genuine expressions of emotion — and thus emotions themselves — can become a more or less deliberate “extravagance”. One might declare his love by threatening to play piano in public ad infinitum, another might proclaim their grief by self-harming. Are genuine or faked emotions behind such activities? It seems to me the question should be how appropriate such emotions and expressions of emotion are in the circumstances. The appropriateness in question is not moral so much as “theatrical”. Is this agent “playing to the gallery” or “laying it on with a trowel”? James Joyce expressed this idea brilliantly when he characterized sentimentality as “unearned emotion”.