Karl Marx argued that what typifies any society is its "mode of production." This is,essentially, the set of relationships between those who own the means of production and those who do the work. Capitalism is a mode of production. So is feudalism.
Marx also argued that there was a mode of production that was peculiar to Asian societies. In this mode of production, private property did not exist. Instead, there were villages that owned the means of production collectively, and a centralized and despotic government that typically takes labor and products directly from the villages. The villagers would be forced to give tribute to the central government and, usually, to provide labor as well. Outside of these interactions, the central government generally let the villages alone.
Marx himself stopped using this term after his early writings. It resurfaced to some extent in the early Soviet Union, but then was expunged from orthodox Marxist-Leninst thought because it was believed that the idea could be used to criticize the Soviet system.