Water in a waterfall has a great amount of mechanical energy. So does a car traveling down the interstate. Mechanical energy is always associated with motion or something that is moving. Heat energy is caused by the motion of particles that make up matter. When you rub your hands together, you are converting mechanical energy into heat energy.
Chemical energy is the energy released when atoms bond together.
The fuel in a rocket engine has stored chemical energy. When the fuel is ignited the fuel's stored chemical energy becomes heat energy and mechanical energy. When you throw a ball you are also using stored chemical energy and turning it into mechanical energy. Nuclear energy is the energy produced in the nucleus of an atom. When the nucleus of an atom splits, nuclear energy is produced in the form of heat energy and light energy.