This all follows from Faraday's law of induction. This explains why the primary has a voltage, and the secondary has a voltage, yet there is no interconnection between them. The overall result is better voltage regulation, minimized line loss and reduced wiring costs. This eliminates separate circuits and independent metering for power and often results in substantial savings. Installing transformers provides a means of subdividing circuits to accommodate independent demand.
Transformers permit grounding of each low voltage circuit.
They are very similar to isolation transformers with one important exception. In an auto-transformer the primary and secondary windings are electrically common to each other. The advantage of using an auto-transformer over an isolation transformer is its smaller size and lower cost. The major disadvantage is no isolation between the primary and secondary which allows noise on the power line to be directly coupled to the load. One last disadvantage is that auto-transformers provide no regulation.