Opposing characters are common in many films, it adds tension and surprise to the story as you don't know when one or another might make a move on the other. To the audience it can be what draws them towards it and attracts them to the story, for example Captain America: Civil War draws the audience to the feud between Iron Man and Captain America which drives the entire story within the film and builds up to a huge vs finale. The same with Harry Potter and Lord Voldemort, the entire film series is driven from the opposition of the two characters, the light and the dark trying to destroy one another before the other gets the chance. With the tension of opposition in films, it is either the central to the storyline or a side story to the film, it creates a good vs evil feel to the film and adds to the theme and action of the film.
Biff Tannen is the opposing character to Marty McFly, he is the bully to Marty's father, George McFly in his youth and still continues to boss him around as an adult. When Marty time travels with the Doc, he continues to encounter Biff in his youth and in age, each time he proves as an obstacle for Marty in his adventure. Although the feud doesn't drive the story like in CA: Civil War or Harry Potter, their opposition affects his family and lifestyle. In the past, Biff proves as an obstacle when Marty is trying to get his parents together to confirm his and siblings births, he bullies George McFly, making him avoid asking Lorraine to be his date which Marty encouraged him to do. In the future, Biff alters time by providing his younger self with betting results, making him rich and controlling his life the way he wants it, this again makes another obstacle for Marty in his aims and causes him to have to go against Biff and his actions to correct time in the present. Marty essentially helps to put Biff into his place but he keeps coming back trying to oppose Marty and what he's doing.
At the end of the film, Marty returns to his present and finds that his interference in the past with the feud between George and Biff resulted in something good for his family, whereas before his mother was an overweight, depressed alcoholic, she is now happy, a healthy weight and happily married. His father is more confident and runs his own business rather than working for Biff, Marty then goes around front of the house to find out the George is Biff's boss and he cowers to George's confidence and demands asap. Their feud clearly adds that extra part needed for the film, adding that one to one action within the film and giving it the side story it needs to make the film more action packed and lively.