I just looked up Lebensram in Wikipedia. I did not know the Germans had a name for their land use policies. Looks like they were on the cutting edge of land use policies, the New Urbanism, and controlling Urban Sprawl. Now I see where todays land use Nazi's get their inspiration.
Yes, basically Lebensraum means "room to live" in German. Hitler argued that the French, the Brits, and others had grabbed all the colonies and that Germany got left out (which had also been one of the grounds for German resentment in the First World War). So, his solution was to conquer the world, kill all the Jews, blacks, Poles, and other "inferior" races, and make more room for Germans to live in.
Incidentally, that's also one reason why Mussolini tried to conquer Ethiopia, because he thought the Italians had also been short-changed in the race for colonial possessions.