No it's not solid or liquid just the movement of electrons along a conductor. At the moment electricity can only be stored as electrical current in superconductors. It is stored conventionally in other forms of energy, Electrical charge in a capacitor or as chemical energy in a battery. More mechanically it is used to pump water to a higher level then when more electricity is needed the water is released to drive generator turbines.
it is very difficult to store electricity (because the free electrons inevitably go places).
in a capacitor, a small component in lots of electrical items that stores charge, it is stored as the energy of the electric field between the two plates of the capacitor.