Lyric discussion by RogueWC 

Cover art for Swimming lyrics by Florence + the Machine

The singing and swimming are the feeling of elation, utter joy, such as found by being in love with someone or a singer singing or being buzzed (drunk or punch-drunk). But after a moment of elation are one must return to their usual state, often followed by a feeling of loss or depression (sinking, drowning). A bit like being addicted to a person as if they were a drug, but that analogy is used too often in modern culture, so this is a more artistic way of looking at it. Learning to get over that loss and looking forward to creating positivity in your own life restore a life to a happier state of normal and allow moments of elation in remembrance of the initial joy. This is akin to overcoming a drug addiction, but in the song it is an addiction to a person.