Shankara wrote the first verse of this sweet song when he was passing through a village and saw an old man memorising the rules of grammar. He felt pity for this old man who was on his deathbed: he had wasted his whole life and now he was wasting his last moment too. All his life he had never remembered the divine and even now he was busy with grammar. What would he gain by memorising the rules of grammar?
Bhajan, devotional singing, kirtan, divine songs and dance are all means of expressing feelings. Shankara is implying that without saying anything you yourself should become a song, a divine song. These verses are very simple, these sutras are straightforward, and they are written by a genius like Shankara. In all of Shankara's literature there is nothing more precious than Bhaj Govindam. Shankara is basically a philosopher; everything he has written is very complex; it is all words, scriptures, logic, analysis and thought. But Shankara knows that godliness cannot be achieved through logic, analysis and thought. The way to attain it is through dancing and singing - through feeling and not through thinking.