Plants grow through photosynthesis,
in which they use sunlight and a chemical inside their leaves called chlorophyll to convert carbon dioxide and water into glucose and oxygen. Write that out chemically and you get this equation:
6CO2 + 6H2O → C6H12O6 + 6O2
There's no mention of "soil" anywhere in there—and that's all the proof you need that plants can grow without it. What they do need is water and nutrients, both easily obtained from soil. But if they can get these things somewhere else—say, by standing with their roots in a nutrient-rich solution—they can do without soil altogether. That's the basic principle behind hydroponics. In theory, the word "hydroponics" means growing plants in water but because you can grow plants without actually standing them in water.