Formal language or style is what is used in most writing and business situations. It does not presume there is a personal or intimate relationship.
For example, while there is nothing grammatically incorrect about most verb contractions, they should be avoided in formal writing unless a personal statement is being directly quoted. They would be a sign of either a more casual attitude towards the reader or a close personal relationship with the reader.
One simple guideline that helps many times--if you ought to type it, it's formal.