People use "Well," at the beginning of a sentence when answering a question. It shows that you're thinking about your answer.
There are other reasons for using "well". You can use it when you're unsure of what you're going to say. You make the word longer and pause before your next word when you're not sure. When you are sure but just want to show that you're thinking about your answer, say "well" quickly and then continue with your answer directly.