In plain words
Kaśyapa made an offering of his all to God and went on experiencing Ānanda. One day his wife Aditi: “My lord! You have offered everything to God. Could you not ask God to grant us a child who can crush the pride of the demons?” she said. In answer to their prayer, Viṣṇu Himself was born in Aditi's womb as Vāmana.
Emperor Bali performed a great many yajñas. But however many yajñas he performed, he gained no peace of mind, and no contentment came to him. After performing a hundred and seven yajñas, he undertook the Viśvajit yāga as the hundred and eighth yajña. At that time Viṣṇu came to him in the form of Vāmana. When Emperor Bali asked, “Master! What would You have?”, Vāmana said, “Sir! It is enough if you give Me three paces of ground as a gift.” Bali promised to give it. His guru Śukrācārya: “Bali! This is no ordinary person; He is very great, one born to Kaśyapa as the gift of a boon. You take Him for an ordinary brahmin. No, no. He has the power to hold the very universe in His grasp. Not merely three paces: He can take over even the three worlds. It is not good for you to set about giving a gift to such a one,” he warned. Emperor Bali was a man of pure heart. Once he had given his word, he would never forget it in the least. That is why he turned to Śukrācārya: “Gurudeva! Is there any death worse than giving one's word and breaking it? I have given my word. So I am ready to give Him whatever He asks. Not only that. Even the hundred and eight yajñas I have performed I will offer at His very feet,” he said, and going up to Vāmana he took hold of His feet, made those hundred and eight yajñas into a garland and put it around His neck. (Swami created a golden necklace of gems with a wave of His divine hand and, showing it to the devotees, said this:)
In this, each gem stands for one yajña. All these are the hundred and eight yajñas.