The manuscripts arrive
Brian Hodgson, based in Nepal, and George Turnour in Ceylon sent Sanskrit and Pāli manuscripts to European libraries in quantity. Working from them, Eugène Burnouf published his Introduction à l'histoire du buddhisme indien in 1844: the first serious scholarly account of Buddhism built from Buddhist texts rather than from travellers' reports.
Translation and the Pali Text Society
Thomas Rhys Davids, who had learned Pāli as a colonial official in Ceylon, founded the Pali Text Society in 1881 with his wife Caroline to edit and translate the Pāli canon. It is still publishing. Max Müller's Sacred Books of the East series carried Buddhist texts to a wide readership, and Viggo Fausbøll's edition of the Dhammapada in 1855 came with a Latin translation, which gives an idea of who was expected to read it.
What readers made of it
Schopenhauer found his own pessimism confirmed and said so loudly. Edwin Arnold's long poem The Light of Asia, published in 1879, told the Buddha's life in Victorian verse and sold in enormous numbers. The Theosophists Olcott and Blavatsky took Buddhist vows in Ceylon in 1880 and then campaigned for Buddhist schools there.
The Buddhism that Western readers met was assembled from ancient texts, with very little contact with any living Buddhist community. Some of the assumptions formed then, that Buddhism is essentially a philosophy, that meditation is its core, that ritual is an accretion, are still with us.
Why it matters
Western readers can engage with Buddhist texts directly, on a wide scale, for the first time.
History and tradition
What historians can say
Nearly all of this is documented in publishers' records, society minutes and the scholars' own correspondence. The texts themselves were often edited to a high standard, and modern translators still work from those editions while disagreeing with the framing around them.