Lorentz invariance — UPSC CSE 2006 Physics PYQ

What do you mean by a gauge transformation ? What is its importance ? Show that the Lorentz gauge condition \vec{\nabla} \cdot \vec{A} + \frac{1}{c} \frac{\partial \phi}{\partial t} = 0 is Lorentz invariant. Here \vec{A} and \phi are the vector and scalar potentials.