Macbeth wrote his letter to tell Lady Macbeth what happened as soon as he won the battle.
His desire of becoming king is so strong and important for him that he makes his wife believe that this wonder, does not come from himself but from something metaphysical, in this case the three witches. He thinks to be more important than ordinary people. Only Macbeth can see them because thay are a product of his imagination; indeed when someone interumpts him while he is seeing the witches, they vanish. Moreover he calls them “sisters” to show that there is a real connection beetween the three witches and himself and because they are “relatives” they have something in common this is why he is the only one who can see them.
The reader can understand Macbeth was not sure to take his decision so he asked his wike what she thought about his wonder. Shakespeare wanted to underline the characterization of one of the women in the Middle Ages. In this period, women had to stay home to make the housework and they did not play a social and political roul. Sometimes, Shakespeare told us that there are the (political) decision “behind” a man.
The letter is arranged in two parts: the first one is about the meeting beetween Macbeth and the three witches after the battle and what they told him about his future; the second one speaks about what will be happen in the future. Shakespeare wrote the letter with a lot of superlative and positive words.