Quote by cygnet1
What does U(1) gauge symmetry mean? Does anyone have a simple explanation?

In physical terms it means that the partial differential equations are insensitive to boundary values of the potentials. Since the Maxwell equations are founded on U(1) symmetry they give you gauge freedom for the potentials.
Equations which comply to SU(2) symmetry for example, as often used in QM, are sensitive to boundary conditions for potentials.