Listening describes an intentional activity. When you are listening, you are actively trying to hear something and you are paying attention to what you hear. Hearing is something that happens without any intentional effort. You can hear something even when you don't want to hear it and don't try to hear it.

If you "hear" something, you know that a sound has been made, and can often recognize what it is, ex: Did you hear that noise? If you "listen" to something or someone, you pay attention to the words, sounds or music that they are making, ex: Could you repeat again; sorry, I wasn't listening. Source: Longman Dictionary

"Listen"= to hear and then mentally process what you hear. Examples: 1. In conversation, listening is preferred to hearing as it means one truly values the meaning behind the words said. 2. I like to listen to country music because the lyrics are interesting. "Hear"= to acknowledge a sound/ the process of sound entering one's ear. Examples: 1. You may hear someone talking, but you may not understand the words or care to listen. 2. I hear the siren of an ambulance in the distance. On the other hand, sometimes people say phrases like "I hear ya!" as an easy way of communicating "I am listening to you and understand!" This context would not be the same as the examples above. Source: self (American English)