Do you know that whenever energy is added to the system, the system gains mass?
Is there any example of conversion of energy to mass and vice - versa? Yes.
A spring's mass increases whenever it is put into compression or tension. Its added mass arises from the added potential energy stored within it, which is bound in the stretched chemical (electron) bonds linking the atoms within the spring.
Actually neither mass gets converted to energy nor energy gets converted to mass. Both are equivalent to each other. If you have some energy E, then you also have mass E/c^2. Similarly, if you have mass m, you have energy mc^2. So, when a high energy gamma photon converts to an electron and a positron in the presence of a nucleus, some books wrongly say that energy has got converted to matter. The right thing is: Total energy of the gamma photon, E= h nu has mass h nu/c^2 and is equal to 2 m c^2/sqrt(1-v^2/c^2) where m is the rest mass of the electron, and v is the speed of electron (positron) in the rest frame of the nucleus.
Let's look at the reverse example.
An atom is made up of number of protons, neutrons and electrons. Each element has a mass associated with it. So logically the mass of an atom should be equal to the sum total masses of all three elements multiplied by the number of such elements present in the atom. Surprisingly, it is observed that the mass of an atom is less than the sum total masses of all elements. Where does the mass go? This mass is converted in to Energy called Binding Energy of the atom and this energy keeps the protons bound together in a nucleus which otherwise should have dismantled in to the environment due to strong repulsive forces between protons. Thus mass is converted in to the energy.
There are many more such examples in the wonderful nature and physics does the job of discovering and explaining such phenomena. In short Physics is Life and Life is Physics.