DO NOT respond directly to the email with your information.
I cannot stress that enough: DO NOT respond to the email with any valuable information. If you decide to send them the CVV number to process the order, go to their website (do not click on a link in the email), and reach out to them using a customer service email or "Contact Us" number and ask them directly if they have requested this information. If they did, call them over the phone and share the CVV that way, rather than in an email.
This sounds like it could be phishing, where a scammer pretends to be someone you've done business with, and asks you for information that can be valuable. Usually it's for a bank user name and password ("Your password has been compromised. Click here to reset!" -- Never ever click there). If we're honest, I don't think this is phishing (a scammer would need your CC details for the CVV to be of any use), but it could be and it's important to develop safe habits.
A merchant uses that code to process the payment and verify possession of the card if they aren't handed the card in person (i.e. internet purchases). So if they didn't ask for it before, that was probably a mistake and at the very least opens them up to more liability. If they're new to accepting credit card payments, it's possible that they're still figuring everything out and it's an honest mistake. But that's the sort of thing they really should figure out after running a couple of orders (of course, a scammer would have that figured out too, so I wouldn't consider that a red flag per se). (NB: Apparently, the requirement isn't as strong as I originally thought (see comments), but I would consider needing the CVV the norm)
I might be willing to give them a benefit of the doubt if it's a new and small operation (and more businesses have become internet based the last few months for obvious reasons), but I'd be extremely wary of responding directly to the email with any personal or remotely valuable information for the reasons stated above. Reach out to the company directly through the website to confirm, preferably with a phone call. It's not perfect, but much more secure with hopefully just a little more effort.