In some ways, Primrose is just a MacGuffin: a device used to move the plot forward instead of a character in and of herself. Katniss has guarded Primrose ever since their father died, and when little sister is chosen in the Games, Katniss leaps to her defense.
There's not much to her in this first movie, except that she's kind-hearted and good. (Witness her keeping a cat alive and fed in the midst of starvation conditions.) She's also terrified of the outside world, which Katniss resolves to save her from.
Beyond that, though, she more a source of motivation than an actual character, which is why we don't see much of her once Katniss volunteers.