To hear the speaker tell it, his father just couldn't stop singing. His singing also apparently gave him amazing super-powers, with which he could control the very forces of nature. (Wow, he should've been in The Avengers or something.)
Okay, okay, we're guessing the speaker doesn't want us to take the way he talks about his father's singing literally. Instead, he uses it as a way to describe his father's joy for life and the way that the father had the ability to inspire others.
Line 3: The first mention of the father's amazing pipes comes when the speaker describes him as "singing each morning out of each night." To us, this seems like a cool way of saying that the father made the best out of bad situations, or could turn negative emotions like despair into good ones like hope. Dark night is usually associated with bad stuff, and the speaker's father uses his amazing singing abilities to transform it into bright morning.
Line 20: The speaker's father does some singing later on, but this time he's "singing desire into begin." We interpret this one to mean that he helps people take their dreams and make them come true. Instead of people just sitting around wanting something, the father helped them begin to actually go for it. In our minds, the motif of singing here is a big part of what saves the line from being cliché.
Line 21: The speaker just can't stop telling us about his father's singing. Later he says that "joy was his song and joy so pure." Unlike most lines in this crazy poem, this line doesn't take a lot of time to interpret. The father's song is happy, like… really happy. It's so happy that joy was an inherent part of its melodies. It's easy enough to translate that to mean that the speaker's father lived his life with joy.
Lines 50-52: The motif of song merges with the imagery of the seasons when the speaker describes his father as "singing each new leaf out of each tree" and goes on to say "every child was sure that spring / danced when she heard my father sing." Here, the father's joyful song is again bringing the renewal of spring in kind of the same way he brought morning out of night before. The stuff about the children dancing seems to be yet another way to say that the father inspired those around him.