When you plug a lamp into an AC outlet, the electrons of the copper wires are forced to vibrate back and forth. They are travelling vibrations in the air. Whenever electric charge moves or flows, that is an electric current. When the quantities of positive and negative charge aren't perfectly equal, there is an imbalance of charge. When positive charges attract negative charges, there is an electric field joining the charges together.
Electric fields are a lot like magnetism.
Both are invisible, and both can reach across empty space and cause things to attract or repel. They are a whole different thing from magnetism. Charged objects create electric fields in much the same way that magnet poles create magnetic fields. To produce a very high voltage, rub a balloon on your head, or scuff your shoes upon the floor when the humidity is very low. Electric fields can push or pull upon electric charges, so electric forces are caused by voltage.