The word "reply" usually refers to some form of verbal or written communication. So when someone has said something to you, and you say something back, you would usually use the word "reply".
The word "answer" is a bit more open. It can mean something you say / write, or it can mean an action you take in response to something someone has said, or in response to a situation. Whereas reply almost always only refers to communication.
Hope that makes sense and helps a little!
Tip: When you respond to a question, its natural speech to say you "answered" the question rather than "replied to" the question.