An electrical connection between discrete points allows the flow of electrons (electric current). A pair of connections is needed for a circuit.
Between points with a low voltage difference, direct current can be controlled by a switch. However, if the points are not connected, and the voltage difference between those points is high enough, electrical ionization of the atmosphere will occur, and current will tend to occur along the path of least resistance.
References
Electrical connection Wikipedia(Text) CC BY-SA