I will try to explain it with an example to you. All higher living organisms need oxygen to survive. Oxygen is required for a process called respiration. So all the aquatic animals like fishes and animals living underground like earthworms would die if oxygen was not dissolved in them.
Generally the amount of oxygen in water is less (5-6 parts of oxygen per million parts of water). This oxygen escaping water can be seen by the simple water heating experiment as explained by Helen.(Try it yourself, you will definitely understand).
Soil by its very structure is porous, i.e., it has small pores in it. The fact that solids may have air dissolved in it can be seen in the case of pumice stone. Pumice is a rock, but it floats on water because it has lots of amount of air dissolved in it, thereby making it light. Soil is also obtained from rocks and is solid. It has minute pores which has oxygen in them.