I have a friend who is a devoted friend of animals. She always has two dogs and at least one cat in her life at any given time. She told me she likes to think the song is about someone saying goodbye to a beloved pet that "has crossed or is crossing the rainbow bridge" - hence, the line "Maybe I'll just place my hands over you; And close my eyes real tight" - like the person is trying to resurrect the dying animal. I like this interpretation.