How does the law of conservation of energy explain magnetism? The law of the conservation of energy describes that energy cannot be created nor destroyed however in fact only changes form. 
How does this law explain the energy transferred by magnetic fields?
 A: Magnetism is not explained by conservation of energy. But magnetism is consistent with conservation of energy.
It is commonly stated that the magnetic field does no work. It is true that the magnetic field does no work on charged particles through the Lorentz force law. The force delivered on a charge due to a magnetic field, $\vec{F}=q \vec{v}\times \vec{B}$, is always perpendicular to $\vec{B}$
However, the magnetic field can do work on the electric field, through one of Maxwell's equations: $\frac{d \vec{E}}{dt}=\frac{1}{\mu_0 \varepsilon_0}\nabla \times \vec{B}-\frac{1}{\varepsilon_0} \vec{J}$
So this is one way in which the magnetic field does work. For example, if you have an inductor in a circuit, a constant current produces a constant magnetic field inside the inductor. Once you switch the current off, you actually get some energy back out of the inductor due to the collapsing magnetic field. This is an instance where the magnetic field does work on the electric field, and the electric field in turn does work by creating a current in the wire.
A: Magnetic fields work like springs.
So for permanent magnets one can align the magnetic dipole moments of the involved subatomic particles and "freeze" this state. But themagnet is than under iner pressure and it is not advised to drop the magnet, it will explode in pieces and the contributed energy will be released.
In the case of the Lorentz force the magnetic dipole moment of moving electrons get aligned under the influence of an external magnetic field. During the deflection of the electron it emits photons, gets dissaligned again and by this the external magnetic field is unchanged again. After the moving electron cames to rest the external magnetic field is the same as at the beginning.
It has to be keeped in mind, that magnetic fields do not interact with electric fields and that they stay unchanged after Lorentz force applications. 
