I can't say what it is in the poly community, but the general jist of it as I have been able to ascertain, is that an emotional affair is:
When you develop a very tight emotional bond with another person whom you find attractive in some way, usually it is only considered an affair once it hits a point where this bond is to the detriment of the bond with your partner.
It is more than a simple crush.
Signs it might be an emotional affair:
You prefer to talk to that person over your partner about emotional problems/issues.
You talk to that person about relationship problems you are having with your partner and NOT talk about them with your partner.
You spend time with that person when your partner would have liked to spend time with you. (and don't address the issue and correct it)
You are ignoring your partner's needs in favour of this friendship.
I'm no expert, I just Googled it a while ago because I wasn't sure.
Male, married, new here, not quite poly. (but poly curious)