Ross is a flat character throughout "Macbeth." He does not have a large part, and his emotions do not affect those of the other characters around him.
In Act I, Scene 3, Ross brings information to Macbeth. Macbeth has been named Thane of Cawdor by Duncan. This proves the witches' prophesies.
Later in the play, after Duncan's death, Ross makes note of the strange things he has seen, which he believes to be a result of the king's assassination.
Other than these two specific examples, Ross' main purpose is to deliver messages of death to the effected families.