Is it true that the nitrogen cycle is the cycling of nitrogen between the atmosphere, soil, and organisms?  

The nitrogen cycle is a biogeochemical process through which nitrogen is converted into many forms, consecutively passing from the atmosphere to the soil to organisms and back into the atmosphere. It involves several processes such as nitrogen fixation, nitrification, denitrification, decay, and putrefaction.

Hence, the nitrogen cycle is a repeating cycle of processes during which nitrogen moves through both living and non-living things: the atmosphere, soil, water, plants, animals, and bacteria.