A "reply" is an answer to a message. When you send a message to someone and they send one back, that return message is their "reply".
This word is similar to "response", and in many situations you can use both. But a "response" is more general than a "reply". A "response" to a message can be a written reply, something that the person said, or even an action like smiling or crying. But a "reply" is usually just a written response.