Short answers, pulled from the story.
Tolkien wrote Mythopoeia after a discussion on the night of the 19th of September 1931 at Magdalen College, Oxford, with C.S. Lewis and Hugo Dyson. Lewis had argued that myths were lies, even if "breathed through silver," and Tolkien composed the poem to defend and explain myth-making as a creative art.
The poem is addressed to C.S. Lewis, identified in the text as the "Misomythos" or myth-hater. The dedication states it is written to one who said that myths were lies and therefore worthless, even though breathed through silver.
Mythopoeia means myth-making. The word has been used in English since at least 1846.
The complete poem was first published in the 1988 edition of Tree and Leaf.
In Mythopoeia, Tolkien describes human creative authors as "the little maker" wielding a "small golden sceptre" over their subcreation. Subcreation refers to genuine creative work carried out within God's primary creation, a framework Tolkien developed further in The Silmarillion.
The poem's refusal to bow before the Iron Crown has been interpreted as Tolkien's opposition to misplaced faith in rationalism and technological progress. In The Silmarillion, Tolkien placed the stolen silmarils inside the iron crown of Morgoth, a Luciferian figure, extending this theme into his mythology.