The rhizosphere is the area in the soil found directly around the roots. It also includes any supporting microorganisms like bacteria, fungi and nematodes.
For example, this is where you will see mycorrhizae forming a symbiosis with the roots of your tree or shrub. The exchange will help the plant's roots better utilize water and survive droughts more often. They are also able to more easily access nutrients in the soil.
Another example of an interaction in the rhizosphere is allelopathy. Some plants put out chemicals through their roots that can harm many other plants' roots and keep them from growing. The black walnut does this by sending out a chemical called juglone.