Hands down, the biggest change between the book and the movie is the reaction to Rue's death. In the book, Katniss only know that she receives a token of District 11's appreciation for her kindness in the form of a gift dropped into the arena. In the movie, the complete reaction of District 11 is brought into greater focus.
After watching their young tribute die at the hands of a vicious killer, the people of District 11 begin to revolt against the Capitol officers who watch over them. They fight against the government that has taken one of their own and sent her into a battlefield to die for their viewing pleasure. In the books (and the movies) this fight against the Capitol is explored in greater depth during the sequels, where Rue becomes something of an iconic figure.