When applied to natural resources and human activity, sustainability refers to practices that will achieve a given economic or social goal without excessively depleting the natural resources available in an area.
For example, sustainable agriculture is agriculture that does not deplete the soil or otherwise cause a given area to become unsuitable for agriculture in the long run. For example, agricultural practices that try to reduce erosion are sustainable. By contrast, a type of agricultural practice that allows topsoil to be carried away by wind and/or water is not sustainable because this practice will deplete the soil, causing the land to no longer be fertile.
Sustainability also refers to other economic activity. The main idea simply is that sustainable economic activity is activity that does not destroy the natural resources needed to carry out that activity.