Hydroponics is first and foremost gardening without soil!
But plants need to be supported somehow and this is accomplished using non-organic materials that are inert and provide easy access for the plants to oxygen and nutrients. The aim is for the medium not to effect the nutrients in any way so that their chemical makeup remains intact.
Coco, LECA, and perlite are the main contenders, using these or a combination of them will suit nearly every growing need.
Aeroponics and NFT - Nutrient Film Technique - dont use a traditional growing medium at all.