Penguin was founded in 1935 by Allen Lane. Lane (who was an editor for and part owner of The Bodley Head, a publisher of hardback books) felt that cheap, small-sized and high-quality books would target a completely different part of the reading market. Especially the lower classes, who could not afford expensive hardback books, would find paperbacks very appealing, more so because the only other publications within their budget were of inferior quality, both in regards of content as packaging.
Lane started out with ten titles, which were so succesful he quickly had to print many more.
Penguins were easily distinguished in shops and on newsstands, because of their size, vivid design (orange would be the main colour on most Penguins for years to come) and clear typography. The first Penguins were reprints of succesful hardback books, but eventually original work was also published.
After starting out with fiction, Penguin soon branched out into other areas of interest. Non-fiction, travel, biography, poetry and all sorts of genres were tried, often with enduring effect.

Recommended Reading
Phil Baines, Penguin By Design: A Cover Story 1935-2005 (Penguin, 2005)
Steve Hare (ed.), Penguin Portrait: Allen Lane and the Penguin Editors 1935-1970 (Penguin, 1995)
Linda Lloyd Jones and Jeremy Aynsley, Fifty Penguin Years (Penguin, 1985)
Jeremy Lewis, Penguin Special: The Life and Times of Allen Lane (Viking, 2005)
J.E. Morpurgo, Allen Lane: King Penguin (Hutchinson, 1979)