The Spring of Arda was a time period before the Awakening of the Children of Ilúvatar.
In this period before Elves appeared, the Valar had ordered the world as they wished and rested upon Almaren (their first kingdom), and Melkor lurked beyond the Walls of Night. During this time, the Vala Yavanna planted the seeds that she had long prepared and the first plants and forests started to grow. Animals as well as many other beasts appeared as well roaming and traversing the new world.
Afterwards, the Valar rested allowing things to take stock of themselves enjoying the fruits of their labors and the bliss of the new world. Then the Valar made a great feast and celebrated as Tulkas married Nessa and things were merry. Tulkas then began to sleep.
It was at this time that Melkor, a form with a sense terror and malice that only the Valar have ever seen decided to return to Arda settling in the far north where the light of Illuin was dim. There he began delving the deeps of a great fortress known as Utumno and from there he made his plans to despoil the works of the Valar. He blighted and poisoned the earth causing living things to fall sick and rot. Knowing that it could only be the work of Melkor, they began to search for him but Melkor was already prepared and before they could find him, he struck destroying the two Lamps of the Valar.
The casting down of the great pillars of the lamps threw the seas into chaos and so also set the world ablaze, as great flames poured out from the lamps. The world was broken and the Valar could not deal with Melkor because their greater strength was needed to restrain the tumults of the world.
The Spring of Arda was over. Almaren was destroyed so the Valar moved to the far western continent and made it their home. There they fenced themselves in and created the Two Trees for light. A new era had begun.