I guess that song is about when you're in a relationship and it's going really well and you're really happy and maybe you have given up parts of yourself. To fall in love and be in a relationship for a long time is like giving a lot of parts of you away because the relationship becomes more important than you as individuals. It's a bit of a tricky balance. I think everyone in a relationship needs to know not to forget themselves..." (from Björk's interview by David Hemingway).
She also explained how the song relates to the hiding of an aggressive part of oneself from a lover.
Basically, 'Hyper-ballad' is about having this kind of bag going on and three years have passed and you're not high anymore. You have to make an effort consciously and nature's not helping you anymore. So you wake up early in the morning and you sneak outside and you do something horrible and destructive, break whatever you can find, watch a horrible film, read a bit of William Burroughs, something really gross and come home and be like, "Hi honey, how are you?".