A nice way to describe physical systems is through
the

Lagrangian formalism. The dynamical equations
of the formalisim take the form of a
variational principle. Any

infinitesimal symmetry transformation that leaves the

action unchanged need not leave
the variation of the action unchanged. In order that
this must vanish when the change in the infinitesimal
is constant we require that the fields to which we
are applying our transformations obey a conservation law.
Conservation laws come from symmetry, this is

Noether's theorm. Examples: