If your question is "what does each cell depend on in its environment," then the answer would be anything that helps the cell maintain homeostasis (keep a balanced internal environment). This could include optimum temperature, pH value, ionic concentration, food supply, oxygen/ carbon dioxide levels, etc.
If your question is "what does each cell's function depend on," then the answer would be the cell's structure. Much as the structure (shape) of your digits (fingers) enables you to perform the function of typing, so does the cell's structure enable it to function in a particular manner. For example, the pseudopods of an amoeba enable the amoeba to engulf and wrap around food. Likewise, the cellulose of a cell wall of a plant cell helps to support and protect the cell.