The girl and young man are trying to escape from the city Ys9 where she's been held for hundreds of years after a spell causing her to stop aging was put on her. The stop aging spell only works whilst she's in the city though but for her to see her special person she has to leave the city and the young man is helping her do it. The older guy chasing them is trying to stop them because he knows that as soon as she leaves the city she'll start aging really fast and die. He's actually her younger brother but appears so old because he was put under the stop-aging spell a good few decades after she was. It is rather confusing haha The important thing is that after being stuck in that city for so long the girl's finally going to follow her dream even though it means her end.