A transformer is a device that changes the electricity to a usable voltage. It is connected to the power station. The three phase transformer has three lines of power connected to the power station's coils instead of one. This makes it more efficient than a single wire system. It is the most common way to produce and transmit electricity.
Delta connections are used when only one type of voltage is needed in short distribution set-ups. Imagine a triangle. The apex is the source of electricity and the two legs are wires to transformer points where that electricity travels. The delta system is not an open system because the two legs are also connected by a wire and both connect back to the apex.
An open delta connection is a delta connection with one leg missing. Imagine the triangle again. Take away one of the wired sides. Only one of the transformer points is connected to the triangle's apex by a wire. Because of the missing wire, this type of connection's power output is less efficient.