Human beings are repeatedly born based on their karma or deeds. God is not influenced by karma, but He also takes various births. Lord Krishna declares in Sri Bhagavad Gita that many births of His have passed (Bahuni mey vyathithani — Chapter IV sloka 5). Vedas also say He takes various births and manifestations (Ajayamano Bahudha Vijayathe). God assigns a valid reason to be born, and the most important is to protect good and pious people and to establish dharma (Parithranaya Sadhunam — Chapter IV sloka 8).
Sri Bharathan Swamy said in a discourse that Lord Krishna, transcending His supremacy, donned the role of an emissary on behalf of the Pandavas. To instil confidence in Sri Sita’s mind, Hanuman, degrading his status, told her in Asokavanam that he himself, though the last and least of the monkey legions, crossed the ocean. Lord Krishna, to boost the confidence of the Pandavas, lowered Himself to the position of a messenger.
The word ‘Sri’ refers to the divine blessings of Goddess Mahalakshmi. It denotes wealth, happiness, prosperity, and great deeds. The word is prefixed to God as Sri Krishna and Sri Rama, as She is ever with Him. Instead of ‘Sri Krishnan Thoodhu’ (Sri Krishna as an emissary), which is to be the standard usage, why is it called ‘Krishnan Sri Thoodhu’? Acharyas like Manavala Mamunigal and Pillai Lokachariar say that the deed of Krishna acting as an emissary is unique and indeed a great one, and hence, it is befitting the title.