A short, oversimplified biography:
Robert Burns was born on the 25th of January, 1759 in Alloway, a village in Ayrshire, Scotland, to a poor but educated farmer. Since the village was too poor to afford a school master, he was educated by his father at home, mostly through the Bible, Milton, and Shakespeare; he taught himself to read French.
By 1784 or so he had taken up work on the farm, the strain of which began the cycle of ill health which would eventually do him in, while writing his poetry on the side. His debut came in 1786, with the publication of the Kilmarnock edition, subtitled "Poems Chiefly in the Scottish Dialect." People like Samuel Taylor Coleridge and Mary Wordsworth took notice, and encouraged him to move to Edinburgh and write full-time. He followed their advice, and by the end of 1787 had moved into a small house there, working as a government tax collector to support himself.
He never liked the social circles of Edinburgh: the aristocracy were far too pretentious, and accepted him only as a rural curiosity, a living curio and example of the theoretical literary ploughman. Burns soon moved away to Dumfries (though he continued as a tax collector there); by then, he was famous enough to be an acceptable husband for his childhood sweetheart (and the first girl he knocked up), Jean Armour, to whom he remained unfaithfully married. Robert Burns died in 1796. His last poem, written on his deathbed to his friend, John Rankine:
He who of Rankine sang, lies stiff and deid,
And a green, grassy hillock hides his heid:
Alas! alas! a devilish change indeed!
Why is Burns famous? After all, some of his stuff is downright awful. Many people like to make the dubious statement that he wrote the first truly modern poetry, experiential and relational. Better than that, he tore poetry away from the artificial language, and wrote in his vernacular. His themes are stolen from the simple world with complex problems; humility, impending mortality, whisky, and women.