I know that they are both pronouns, meaning "I". But people appear to use them in specific situations. How different are they?
Simply put, 나는 is plain form/not formal. On the other hand, 저는 is used as a sign of deference to the person you are speaking with. It is the "humble" form of 'I'.
Use 나는 when you are speaking about yourself in an informal and casual setting, especially if you are speaking with someone who is your junior. If you are speaking with a superior, use 저는.