This statement is more difficult than the concept above, for everyone can comprehend the idea of overfilling a container.
The atmosphere can hold water, and warmer air holds more water than dry colder air. As the temperatures of the Earth rise, more water will evaporate into the air. This is insignificant to abate a sea level rise, but highly significant in other ways.
When water evaporates, it becomes more energetic. The molecules move faster. So, we store more energy in the atmosphere. The warmer the air, the more water it can hold, so the more energy it can have. The energy comes from the higher temperatures, which do cool slightly with evaporation. So some of the energy from higher temperature is changed into evaporating more water.
When a storm forms the air condenses the water. Energy the water vapor held is given back off when the water once again becomes liquid. This energy heats the air, since it no longer is needed to keep the water molecules moving in the vapor state. Warmer air rises, and as a result the lower pressure and cooler temperatures aloft cause the air to have a capacity for even less water vapor. So, more water vapor condenses, causing an even greater release of energy to make the air even lighter, so the process continues.
When liquid water freezes the molecules need even less energy, so the unneeded energy is also released. This enhances the cloud building process.
Eventually, a storm can result.
So, a warmer Earth holds more water vapor in the atmosphere, which is the fuel for storms. Instead of burning the fuel, as with an automobile, the heat engine called a storm is supplied with heat directly from the water vapor condensing into liquid water, and eventually from freezing liquid water into ice.
Making the relationship understandable, we simply must realize water vapor holds energy, which is released as heat to drive storms. The higher the Earth temperatures rise, the more water vapor the atmosphere can hold, which in turn can drive more, and stronger storms. It is a matter of having more fuel.
As an analogy, suppose your automobile were to have a larger fuel tank, and the ability to burn fuel faster. It could go on more trips and at greater speeds. Well, a warmer Earth has a larger fuel tank, which can drive more storms at greater intensity than we now experience.