To sell on eBay (and get paid) you need to have a payment processor.
Until recently that was Paypal, but most sellers have now been moved to eBay's own Managed Payments.
Look at your Seller Hub (My eBay-> Selling-> Orders)
Is there an order there?
If not he didn't buy anything through eBay. Ignore him.
If there is an order there, how do you receive payments?
Tell the buyer to
- Go to Purchase history - opens in new window or tab and find the order he wants to cancel.
- Select the More actions dropdown menu and select Contact seller.
- Choose Request to cancel this order, then Contact the seller.
- Explain to the seller why you need to cancel, and select Send.
This puts the request on eBay's radar and allows you to accept the cancellation which makes the refund automatic.