Potential energy is the energy possessed by a body by virtue of its position or state. Kinetic energy is energy possessed by a body by virtue of its movement.
Law of conservation of energy states that energy cannot be destroyed but can only be transformed form one form into another. KE and PE are interconvertible and hence do not contradict the law of conservation of energy.
PE + KE = Total Energy
ΔPE+ΔKE=ΔTotal energy
total energy of the system will remain constant So ΔTotal energy=0
so ΔPE+ΔKE=0
It means ΔPE=-ΔKE (relation between kinetic energy and potential energy change)
The relation between kinetic energy and potential energy is that we can transform one form of energy into another form,if potential energy of the system will increase than kinetic energy will decrease and vice versa.
Example
Take the example of book sitting on a counter. When the book is at rest, it has potential energy. But, say, when a person walks by and accidentally knocks the book off of the counter, the book has kinetic energy as it falls, because it is in motion and the potential energy has transformed into kinetic energy.