I am not a Coinbase user, but afaik, sending bitcoin to another Bitcoin user will require mining fee but unless the person you are sending to is also a Coinbase customer, if the recipient is a Coinbase user, you will be able to send to the person using email for free. I hope someone that is using coinbase will be able to tell you how to do it.
I think I get it now. So OP is referring to Coinbase<->Coinbase transactions.
I want to know how the transaction is done in email. What is the process
The transaction is not done
through email, it's just that you can send funds to other existing Coinbase users using their email. Also, it's not an on-chain transaction as you would make which has transaction fees. It's just easy and free because Coinbase<->Coinbase transactions are merely just change of balance numbers on Coinbase's database.