Emailable: A person is emailable if they are able to receive blast emails from your nation. This means that they have a valid email address and have not unsubscribed from your communications. Check this by looking to see if "receive emails" is checked, "do not contact, period" is not checked, "bad email" is not checked, and they actually have an email address. If all those criteria are present, the person is emailable.
Bad: If "bad email" is checked, of course. This is checked automatically if the email address is actually invalid, or after sending an email blast the other server tells us that the email address doesn't exist.
Bounced: This means we don't know that the email address is bad yet, but there were problems sending an email to it. The server could be down, the account could be over quota, various issues that could be temporary.
It’s important to remember that the number of emailable people in your database will affect the pricing of your nation. If you want to check how many people within your nation are emailable you can run a filter search.