Lyric discussion by angryhippo 

Cover art for Swimming lyrics by Florence + the Machine

I think "the song" that she is talking about represents a relationship she has with a guy.

Sinking = falling in love swimming = being hopelessly in love although in the song it alludes to something being wrong with the relationship and if you look at the other elements, like an exploding life jacket, and jumping back in the water after seeing him, show that something is wrong

Just some thoughts

My Interpretation