I think this song is about a relationship that fell through because the other person moved away ("New York City/ Had the craze you wanted"). The person (guy) who didn't leave is still holding on to the hope that things haven't changed even though the other moved away. He thinks she still cares about him and he cares about her ("We both know we feel about this/ Are you hanging on? We both know we feel about this/ But you're feeling oh so wrong") and he refuses that they give up... so he's holding on and "walking after" her.
I think this song is about a relationship that fell through because the other person moved away ("New York City/ Had the craze you wanted"). The person (guy) who didn't leave is still holding on to the hope that things haven't changed even though the other moved away. He thinks she still cares about him and he cares about her ("We both know we feel about this/ Are you hanging on? We both know we feel about this/ But you're feeling oh so wrong") and he refuses that they give up... so he's holding on and "walking after" her.