Energy is defined as "the ability to do work" which is a really useful definition…in physics.
In chemistry it is better to think of energy in terms of what it can do. Energy is something that can change matter, but isn’t matter. Changing matter can be as simple as changing it’s shape (think of molding clay), changing it's location (pulling a wagon up a hill) changing it’s appearance (dissolving salt in water), or changing what it is (burning wood to produce carbon dioxide and water).
Energy comes in two flavors, Kinetic Energy and Potential Energy. Kinetic Energy is energy associated with motion. This form of energy is the reason that a speeding car can change the matter of a fence or tree if it leaves the road.
A special form of kinetic energy is called heat. (More information on heat and its relationship with temperature can be found here.) Heat is kinetic energy when the things moving are too small to see. In other words when a baseball is thrown at a wall it has kinetic energy. After the baseball hits the wall, the invisible vibrations it created in the wall when it hit are heat.
Potential Energy is energy that is not associated with motion. It is common to think of potential energy as stored energy, but this is not a terrible helpful idea. In chemistry, it is better to think of Potential energy as energy associated with position. Anything that is attracted to something else and is not in contact with it has potential energy.
An easy example of this idea is to think about gravity. Imagine a cartoon character who has just run off the edge of cliff. They will certainly change their own matter and the matter of the ground when they fall,so they must have energy, but in the cartoon moment before they realize that they are about to fall, they do not yet have kinetic energy because they are not yet falling. The energy is in the attraction they have for the earth (gravity) and the distance between them and the ground.
When two things are attracted and are not together, they have potential energy. The amount of potential energy depends on the attraction and the distance.
Conservation of energy is the idea that energy is never lost. In other words, energy can be transferred from one thing to another or from one type to another but never goes away. When our cartoon character falls from the cliff he falls faster and faster (gaining kinetic energy) while getting closer and closer to the ground (losing potential energy). When he hits the ground and stops, the energy is still not lost (even though he cannot fall further and is no longer moving). At that point the energy is transferred to the ground as vibrations that spread out until they are so small that they can no longer be felt (heat).