While the Thiruppavai has many commentaries, it itself may be considered a commentary on the Vedas, said Malola Kannan, in a discourse. Every pasuram in Thiruppavai reflects the Vedas in one way or the other. Taking the Azhi mazhai kanna pasuram as an example, one can see how it is like Veda sabdas. There are yagas that are performed to obtain the benefit of rains. There are five sabdas prescribed as mandatory during these yagas. If the required yagas are not performed, then it will not rain, and for the yagas to bear fruit, these five sabdas are indispensable. Andal’s Azhi mazhai pasuram captures the essence of the Vedic mantras recited for rains. Similarly, each pasuram can be studied for its Vedic connection. Verse twenty-eight of Thiruppavai (karavaigal pin sendru) may be considered the prayaschitta pasuram. Thiruppavai begins with a vrata, and the twenty seventh verse marks the end of the vrata. Now that the vrata is over, it is time for prayaschittam (atonement). The Gopikas are lucky to have had Krishna in their midst as one of them. The Gopikas might have called Him by names that He might not have liked. Their way of addressing Him might not have been as respectful as it should have been. So, now they are asking Krishna for His forgiveness. For a yaga to be complete and to give the desired results, one must do a prayaschittam. Thiruppavai itself is akin to a yaga and now that the yaga is over, prayaschittam is offered through the karavaigal pasuram. Kanaithilam pasuram is about Vedanta Desika. Just as a cow lets milk flow from its udder, to feed its calf, so did Lord Lakshmi Hayagreeva bless Vedanta Desika. In fact, Desika says in his Hayagreeva Stotram, that the Lord sat on his tongue (jihvAgra simhAsanam), helping him defeat opponents.
Source : https://www.thehindu.com/todays-paper/tp-miscellaneous/vedas-and-thiruppavai/article28631091.ece