Rue is the youngest person in the hunger games. As a tribute from District 11, she is forced to compete with older teenagers that are much stronger than her. During the training sessions, she developes an appreciation for Katniss and the two form an unlikely alliance in the games themselves.
Katniss is particularly interested in protecting Rue because the young competitor reminds her of her younger sister. When Katniss' sister Primrose was chosen to compete, Katniss stood up to take her place, but no one volunteered to take Rue's place - so Katniss feels a certain solidarity with her. In the movie, the connection between Rue and Katniss' sister is largely glossed over. The two still form an alliance, of course, but Katniss' empathy for her is never fully discussed in the film.