Literally "living room", in practice, Lebensraum refers to an idea in Pan-German nationalism that was a major goal of Adolf Hitler. Hitler justified the invasion of the East with the tradition Drang nach Osten, or expansion into Slavic lands to the east of Germany.
The term had been used since the 1890s, often focused on German "alleged overpopulation". Taking Slavic land coexisted with the desire for overseas colonies. It had historical connotations of Teutonic knights of the Middle Ages, taking Slavic lands for Germany.
In Mein Kampf, he wrote "territorial policy cannot be fulfilled in the Cameroons but today almost exclusively in Europe....this soil exists for the people which possesses the force to take it. [if they object]...the law of self-preservation goes into effect, and what is refused to amicable methods, it is up to the fist to take." 
His thinking was influenced, although not a quote, of Karl Haushofer's theories of geopolitics, which treated states as biological organisms, which would expand or contract based on resources, and compete with other nation-organisms for resources. Haushofer saw control of land in territorial Europe as more important than colonies. 
- Ian Kershaw (1998), Hitler 1889-1936: Hubris, W.W. Norton, ISBN 0-393-04671-0, pp. 248-249
- Woodruff Smith, The Ideological Origins of Nazi Imperialism, Oxford, 1986, pp. 110-111 and 164, quoted by Kershaw, p. 248
- William Shirer (1960), The Rise and Fall of the Third Reich, Simon & Schuster, pp. 82-84
- Gearoid O Tuathail (2000), Critical Geopolitics, CRC Press, pp. 35-37