Physics says, when a force is applied on an object and it moves to certain distance, work is said to be done. The capacity for doing work is energy.
A body at a height, can fall down due to gravitational force . So it said to posses 'potential energy'.
A fast moving body can hit another body and do some work. So it has 'kinetic energy'.
Petrol can burn, produce heat, gases expand, pushes the piston of an engine and does some work. Hence petrol has 'chemical energy' (heat energy)
The chemical in the battery reacts and push the electrons from one electrode to another making electric current. So the battery stores 'chemical energy'.
When light falls on certain materials, it ejects electrons. So even light has energy