Organic tissue was the grouped organization of cells that acted as the functionary intermediary between that and organs.
Tissue samples could be stored and preserved in a medical freezer for later use. (ENT: "Terra Prime")
In 2268, after Hikaru Sulu had been touched by the hologram Losira, Doctor Leonard McCoy discovered a layer of necrotic tissue a few cells thick in the helmsman's shoulder. (TOS: "That Which Survives")
When Doctor Beverly Crusher investigated the strange behavior of Admiral Mark Jameson, she found traces of chemical substances in his blood and tissue samples. (TNG: "Too Short A Season")
Muscle tissue was one of the components Chakotay found in a tank aboard a Hirogen ship in 2374. (VOY: "Prey")
In 2375, Doctor Julian Bashir claimed that the Holy Grail of organ replacement would be to come up with a way to inject the patient with undifferentiated tissue that could become whatever organ is needed. He had hoped that he could "borrow a cup of goo" from Odo, so as to study the Changeling's morphogenic matrix, in effort to find the means required to synthesize organic tissue that can change form the way Changeling cells do. (DS9: "When It Rains...")