Sustainable is any activity that is suitable to last as long as the ecological conditions stay the same. A resource management is sustainable when resources are used up in a speed not higher than their regeneration speed. The expression comes from forestry where it means that only as many trees are cut as can come up in the same time. Fishing is sustainable when the number of fish (of the corresponding species) does not incline. The use of fossil fuels or of nuclear energy is practically never sustainable.
A sustainability in economical terms does not necessarily mean that something is environmentally friendly. An oilpalm plantation can be sustainable in a sense that it brings yield which does not cease, but for it vast areas of virgin forest have been cut down, the ecosystems destroyed and the people driven away.
A frequent expression is that of a sustainable development. that is a contradiction in itself; a development cannot be sustainable. There can be, however, a development away from an unsustainable situation towards a sustainable one.
Of course sustainability is a lot older than the word. Many cultures during their history have found a sustainable way of living because unsustainable forms of economy had to come to an end sooner or later. An example: The Maori (a Polynesian nation), when arriving to New Zealand, found huge birds, the moas, and developed a culture based on their hunting for eating the meat until they exterminated the moas. Then they had no other choice than to change their economy. They made agriculture (what they had done before already) and developed a sustainable economy. The differences between the two cultures are so striking that until a few decade ago they were considered two waves of immigration. Today we are convinced that it was only one wave, the Maoris, who were forced to change their economy completely.