Generally an answer is an answer to a question. It can be long and complicated, such as the answer to, "What are the stages of cell mitosis?" or simple as the answer to, " What time is it". The answer generally provides the information needed to satisfy the question. 'To reply' is similar to 'to respond'. If I said, "I don't know" to the question about mitosis, that would be a reply but not so much an answer. I might even reply, "I'm afraid I don't know the answer." One replies to a request whether the answer to the request is 'yes' or 'no'. All that said, there are other uses for these words. One always answers the phone and answers the doorbell although no question is asked.

To reply is to respond to what someone had said. To answer is to respond to a specific question, usually with a solution. The main difference is, a person can reply without answering. For example: If I send a text asking "Hi, How are You?" A reply might be: "What are you up to?" (the person has replied but not answered) An answer might be: "I am fine." (the person responds to the question) However, we often use 'reply' in the same situation we would use 'answer'. I hope this helps. :)