The tone, or attitude, is the way the narrator is trying to get across to make you feel. They are trying to show how they are feeling without directly saying it.
A narrator while offering his or her story in a certain tone. A "tone" is the general attitude or character under which the narrator is while telling the story. This attitude could reflect the mental state in which the narrator is at that moment.
There are some tones that have a better fit according to the genre of the story. A story of war would probably have an energetic tone, whereas a tragedy would have a solemn tone.