The process of growing plants without soil is called hydroponics. Using hydroponics to grow tomatoes means their roots will be suspended in a liquid nutrient solution instead of growing down into dirt.
You can see "water" in the word hydroponics if you look closely: hydro means "water" in Greek. Usually, using hydroponics means that plants grow in water that's mixed with nutrients, although they sometimes grow in gravel, coir, wool, or some other material instead. The ponics part of the word also has a Greek root, ponein, "to labor or toil."