Short answers, pulled from the story.
Ovid attributed his exile to a carmen et error, Latin for a poem and a mistake. He suggested the Ars Amatoria, his manual of seduction, was the offending poem, as it conflicted with Augustus' Julian marriage laws of 18 BC. He was deliberately vague about the specific mistake, which has led to centuries of scholarly debate.
Ovid was banished in AD 8 to Tomis, the capital of the province of Moesia on the Black Sea, now Constanta in Romania. He remained there for the last nine or ten years of his life and died at Tomis in AD 17 or 18.
The Metamorphoses is a fifteen-book poem in dactylic hexameter cataloguing nearly 250 myths from Greek and Roman mythology, organized around the theme of transformation. It spans from the formation of the world to the apotheosis of Julius Caesar, with characters transformed into trees, animals, flowers, and constellations.
In exile, Ovid wrote the Tristia, five books of elegiac poems dated to AD 9-12 expressing despair and advocating his return to Rome, and the Epistulae ex Ponto, four books of letters to friends in Rome asking them to secure his recall. The first three books of the Epistulae were published in AD 13, and the fourth book between AD 14 and 16.
Writers influenced by Ovid include Geoffrey Chaucer, Christopher Marlowe, and William Shakespeare, who encountered the Metamorphoses through Arthur Golding's 1567 English translation. Montaigne, Miguel de Cervantes, John Milton, Dante Alighieri, and Alexander Pushkin also drew on Ovid's work, as did Bob Dylan in his 2006 album Modern Times.
The Ars Amatoria was a three-book didactic elegiac poem published around AD 2 that taught men and women the arts of seduction, positioning Ovid as a praeceptor amoris, a teacher of love. It became controversial because it treated adultery as subject matter at a time when Augustus had enacted the Julian marriage laws of 18 BC to promote monogamous marriage.