Electricity doesn't exist in space in the usual way we think about it, namely electrons flowing in a wire. But that's only because space normally doesn't have wires. If you take something electronic up into space, it will work just fine (as long as you keep it at a normal temperature... space can be super cold). On the other hand, there are a few free electrons and ions in space. An ion is simply an atom or molecule which has lost an electron or gained an extra electron, so it is charged. These charged electrons and ions interact with each other (opposite charges attract) and with the magnetic field of the Sun. If you put a battery out in space, it would cause the electrons and ions to flow. This electrical current would be very weak, however, because the number of electrons and ions is very, very small.