나 and 저 mean the same thing ("I") but belong to different levels of politeness of speech.
나 is part of the casual style used among children and youngsters, when adults speak to children, or in situations where the two people are familiar with each other.
In other cases, like between adult strangers or speaking to people senior to you, you are supposed to use 저.
There is also a whole class of sentence ending forms pertaining to either of these speech styles.